Math: add typedefs for single-row matrices.

May be useful for left-hand-side multiplication, as a counterpart for
multiplying with (column) vectors from the right hand side.

doc/changelog.dox

@@ -77,6 +77,9 @@ See also:
 -   New @ref Range1Dui, @ref Range2Dui and @ref Range3Dui typedefs for unsigned
     integer ranges
 -   New @ref Nanoseconds and @ref Seconds typedefs for time values
+-   New @ref Matrix2x1, @ref Matrix3x1, @ref Matrix4x1 typedefs for single-row
+    matrices as a counterpart for column vectors, together with corresponding
+    double variants and type aliases in the @ref Math library
 -   Added MSVC Natvis files and pretty-printers for GDB. See @ref debuggers,
     [mosra/magnum#589](https://github.com/mosra/magnum/pull/589),
     [mosra/magnum#595](https://github.com/mosra/magnum/pull/595),

doc/snippets/Math.cpp

@@ -1328,6 +1328,19 @@ Float a = m[2][1];
 static_cast<void>(a);
 }
 
+{
+/* [RectangularMatrix-multiply-vector] */
+Matrix3x4 m = DOXYGEN_ELLIPSIS({});
+Vector3 v = DOXYGEN_ELLIPSIS({});
+
+/* a1 and a2 contain the same data, just transposed */
+Vector4 a1 = m*v;
+Matrix4x1 a2 = Matrix3x1::fromVector(v)*m.transposed();
+/* [RectangularMatrix-multiply-vector] */
+static_cast<void>(a1);
+static_cast<void>(a2);
+}
+
 {
 /* [gather] */
 Vector4i original(-1, 2, 3, 4);

doc/types.dox

@@ -86,29 +86,36 @@ after type name means @ref Float underlying type, `h` means @ref Half, `d` is
 
 | Magnum matrix type                                               | Equivalent GLSL type                  |
 | ---------------------------------------------------------------- | ------------------------------------- |
+| @ref Matrix2x1 or @ref Matrix2x1d                                | (*none*) |
 | @ref Matrix2x2 or @ref Matrix2x2d                                | @glsl mat2 @ce / @glsl mat2x2 @ce or @glsl dmat2 @ce / @glsl dmat2x2 @ce |
 | @ref Matrix2x2h, @ref Matrix2x2b, @ref Matrix2x2s                | (*none*) |
-| @ref Matrix3 / @ref Matrix3x3 or @ref Matrix3d / @ref Matrix3x3d | @glsl mat3 @ce / @glsl mat3x3 @ce or @glsl dmat3 @ce / @glsl dmat3x3 @ce |
-| @ref Matrix3x3h, @ref Matrix3x3b, @ref Matrix3x3s                | (*none*) |
-| @ref Matrix4 / @ref Matrix4x4 or @ref Matrix4d / @ref Matrix4x4d | @glsl mat4 @ce / @glsl mat4x4 @ce or  @glsl dmat4 @ce / @glsl dmat4x4 @ce |
-| @ref Matrix4x4h, @ref Matrix4x4b, @ref Matrix4x4s                | (*none*) |
 | @ref Matrix2x3 or @ref Matrix2x3d                                | @glsl mat2x3 @ce or @glsl dmat2x3 @ce |
 | @ref Matrix2x3h, @ref Matrix2x3b, @ref Matrix2x3s                | (*none*) |
-| @ref Matrix3x2 or @ref Matrix3x2d                                | @glsl mat3x2 @ce or @glsl dmat3x2 @ce |
-| @ref Matrix3x2h, @ref Matrix3x2b, @ref Matrix3x2s                | (*none*) |
 | @ref Matrix2x4 or @ref Matrix2x4d                                | @glsl mat2x4 @ce or @glsl dmat2x4 @ce |
 | @ref Matrix2x4h, @ref Matrix2x4b, @ref Matrix2x4s                | (*none*) |
-| @ref Matrix4x2 or @ref Matrix4x2d                                | @glsl mat4x2 @ce or @glsl dmat4x2 @ce |
-| @ref Matrix4x2h, @ref Matrix4x2b, @ref Matrix4x2s                | (*none*) |
+| @ref Matrix3x1 or @ref Matrix3x1d                                | (*none*) |
+| @ref Matrix3x2 or @ref Matrix3x2d                                | @glsl mat3x2 @ce or @glsl dmat3x2 @ce |
+| @ref Matrix3x2h, @ref Matrix3x2b, @ref Matrix3x2s                | (*none*) |
+| @ref Matrix3 / @ref Matrix3x3 or @ref Matrix3d / @ref Matrix3x3d | @glsl mat3 @ce / @glsl mat3x3 @ce or @glsl dmat3 @ce / @glsl dmat3x3 @ce |
+| @ref Matrix3x3h, @ref Matrix3x3b, @ref Matrix3x3s                | (*none*) |
 | @ref Matrix3x4 or @ref Matrix3x4d                                | @glsl mat3x4 @ce or @glsl dmat3x4 @ce |
 | @ref Matrix3x4h, @ref Matrix3x4b, @ref Matrix3x4s                | (*none*) |
+| @ref Matrix4x1 or @ref Matrix4x1d                                | (*none*) |
+| @ref Matrix4x2 or @ref Matrix4x2d                                | @glsl mat4x2 @ce or @glsl dmat4x2 @ce |
+| @ref Matrix4x2h, @ref Matrix4x2b, @ref Matrix4x2s                | (*none*) |
 | @ref Matrix4x3 or @ref Matrix4x3d                                | @glsl mat4x3 @ce or @glsl dmat4x3 @ce |
 | @ref Matrix4x3h, @ref Matrix4x3b, @ref Matrix4x3s                | (*none*) |
+| @ref Matrix4 / @ref Matrix4x4 or @ref Matrix4d / @ref Matrix4x4d | @glsl mat4 @ce / @glsl mat4x4 @ce or  @glsl dmat4 @ce / @glsl dmat4x4 @ce |
+| @ref Matrix4x4h, @ref Matrix4x4b, @ref Matrix4x4s                | (*none*) |
 
 Any super- or sub-class of the same size and underlying type can be used
 equivalently (e.g. @ref Math::Vector "Math::Vector<Float>" or @ref Color3
 instead of @ref Vector3).
 
+Vectors are columns and are usable in all contexts where single-column matrices
+would be, such as matrix multiplication. The @ref Matrix2x1, @ref Matrix3x1 and
+@ref Matrix4x1 typedefs are then their transposed single-row counterparts.
+
 For easier entering of (s)RGB colors in hexadecimal format there are
 @link Math::Literals::ColorLiterals::operator""_srgb() _srgb @endlink /
 @link Math::Literals::ColorLiterals::operator""_srgbf() _srgbf @endlink,

src/Magnum/Magnum.h

@@ -526,22 +526,10 @@ typedef Math::Color4<UnsignedByte> Color4ub;
 typedef Math::Color4<UnsignedShort> Color4us;
 
 /**
-@brief 3x3 float transformation matrix
-
-Equivalent to GLSL @glsl mat3 @ce.
-@see @ref Matrix3x3
-@m_keyword{mat3,GLSL mat3,}
-*/
-typedef Math::Matrix3<Float> Matrix3;
-
-/**
-@brief 4x4 float transformation matrix
-
-Equivalent to GLSL @glsl mat4 @ce.
-@see @ref Matrix4x4
-@m_keyword{mat4,GLSL mat4,}
+@brief Float matrix with 2 columns and 1 row
+@m_since_latest
 */
-typedef Math::Matrix4<Float> Matrix4;
+typedef Math::Matrix2x1<Float> Matrix2x1;
 
 /**
 @brief 2x2 float matrix
@@ -552,30 +540,26 @@ Equivalent to GLSL @glsl mat2x2 @ce.
 typedef Math::Matrix2x2<Float> Matrix2x2;
 
 /**
-@brief 3x3 float matrix
+@brief Float matrix with 2 columns and 3 rows
 
-Equivalent to GLSL @glsl mat3x3 @ce. Note that this is different from
-@ref Matrix3, which contains additional functions for transformations in 2D.
-@m_keyword{mat3x3,GLSL mat3x3,}
+Equivalent to GLSL @glsl mat2x3 @ce.
+@m_keyword{mat2x3,GLSL mat2x3,}
 */
-typedef Math::Matrix3x3<Float> Matrix3x3;
+typedef Math::Matrix2x3<Float> Matrix2x3;
 
 /**
-@brief 4x4 float matrix
+@brief Float matrix with 2 columns and 4 rows
 
-Equivalent to GLSL @glsl mat4x4 @ce. Note that this is different from
-@ref Matrix4, which contains additional functions for transformations in 3D.
-@m_keyword{mat4x4,GLSL mat4x4,}
+Equivalent to GLSL @glsl mat2x4 @ce.
+@m_keyword{mat2x4,GLSL mat2x4,}
 */
-typedef Math::Matrix4x4<Float> Matrix4x4;
+typedef Math::Matrix2x4<Float> Matrix2x4;
 
 /**
-@brief Float matrix with 2 columns and 3 rows
-
-Equivalent to GLSL @glsl mat2x3 @ce.
-@m_keyword{mat2x3,GLSL mat2x3,}
+@brief Float matrix with 3 columns and 1 row
+@m_since_latest
 */
-typedef Math::Matrix2x3<Float> Matrix2x3;
+typedef Math::Matrix3x1<Float> Matrix3x1;
 
 /**
 @brief Float matrix with 3 columns and 2 rows
@@ -586,20 +570,13 @@ Equivalent to GLSL @glsl mat3x2 @ce.
 typedef Math::Matrix3x2<Float> Matrix3x2;
 
 /**
-@brief Float matrix with 2 columns and 4 rows
-
-Equivalent to GLSL @glsl mat2x4 @ce.
-@m_keyword{mat2x4,GLSL mat2x4,}
-*/
-typedef Math::Matrix2x4<Float> Matrix2x4;
-
-/**
-@brief Float matrix with 4 columns and 2 rows
+@brief 3x3 float matrix
 
-Equivalent to GLSL @glsl mat2x4 @ce.
-@m_keyword{mat2x4,GLSL mat2x4,}
+Equivalent to GLSL @glsl mat3x3 @ce. Note that this is different from
+@ref Matrix3, which contains additional functions for transformations in 2D.
+@m_keyword{mat3x3,GLSL mat3x3,}
 */
-typedef Math::Matrix4x2<Float> Matrix4x2;
+typedef Math::Matrix3x3<Float> Matrix3x3;
 
 /**
 @brief Float matrix with 3 columns and 4 rows
@@ -609,6 +586,20 @@ Equivalent to GLSL @glsl mat3x4 @ce.
 */
 typedef Math::Matrix3x4<Float> Matrix3x4;
 
+/**
+@brief Float matrix with 4 columns and 1 row
+@m_since_latest
+*/
+typedef Math::Matrix4x1<Float> Matrix4x1;
+
+/**
+@brief Float matrix with 4 columns and 2 rows
+
+Equivalent to GLSL @glsl mat2x4 @ce.
+@m_keyword{mat2x4,GLSL mat2x4,}
+*/
+typedef Math::Matrix4x2<Float> Matrix4x2;
+
 /**
 @brief Float matrix with 4 columns and 3 rows
 
@@ -617,6 +608,33 @@ Equivalent to GLSL @glsl mat4x3 @ce.
 */
 typedef Math::Matrix4x3<Float> Matrix4x3;
 
+/**
+@brief 4x4 float matrix
+
+Equivalent to GLSL @glsl mat4x4 @ce. Note that this is different from
+@ref Matrix4, which contains additional functions for transformations in 3D.
+@m_keyword{mat4x4,GLSL mat4x4,}
+*/
+typedef Math::Matrix4x4<Float> Matrix4x4;
+
+/**
+@brief 3x3 float transformation matrix
+
+Equivalent to GLSL @glsl mat3 @ce.
+@see @ref Matrix3x3
+@m_keyword{mat3,GLSL mat3,}
+*/
+typedef Math::Matrix3<Float> Matrix3;
+
+/**
+@brief 4x4 float transformation matrix
+
+Equivalent to GLSL @glsl mat4 @ce.
+@see @ref Matrix4x4
+@m_keyword{mat4,GLSL mat4,}
+*/
+typedef Math::Matrix4<Float> Matrix4;
+
 /**
 @brief Signed byte matrix with 2 columns and 2 rows
 @m_since{2020,06}
@@ -1133,6 +1151,12 @@ Equivalent to GLSL @glsl dmat4 @ce.
 */
 typedef Math::Matrix4<Double> Matrix4d;
 
+/**
+@brief Double matrix with 2 columns and 1 row
+@m_since_latest
+*/
+typedef Math::Matrix2x1<Double> Matrix2x1d;
+
 /**
 @brief 2x2 double matrix
 
@@ -1142,30 +1166,26 @@ Equivalent to GLSL @glsl dmat2x2 @ce.
 typedef Math::Matrix2x2<Double> Matrix2x2d;
 
 /**
-@brief 3x3 double matrix
+@brief Double matrix with 2 columns and 3 rows
 
-Equivalent to GLSL @glsl dmat3x3 @ce. Note that this is different from
-@ref Matrix3d, which contains additional functions for transformations in 2D.
-@m_keyword{dmat3x3,GLSL dmat3x3,}
+Equivalent to GLSL @glsl dmat2x3 @ce.
+@m_keyword{dmat2x3,GLSL dmat2x3,}
 */
-typedef Math::Matrix3x3<Double> Matrix3x3d;
+typedef Math::Matrix2x3<Double> Matrix2x3d;
 
 /**
-@brief 4x4 double matrix
+@brief Double matrix with 2 columns and 4 rows
 
-Equivalent to GLSL @glsl dmat4x4 @ce. Note that this is different from
-@ref Matrix4d, which contains additional functions for transformations in 3D.
-@m_keyword{dmat4x4,GLSL dmat4x4,}
+Equivalent to GLSL @glsl dmat2x4 @ce.
+@m_keyword{dmat2x4,GLSL dmat2x4,}
 */
-typedef Math::Matrix4x4<Double> Matrix4x4d;
+typedef Math::Matrix2x4<Double> Matrix2x4d;
 
 /**
-@brief Double matrix with 2 columns and 3 rows
-
-Equivalent to GLSL @glsl dmat2x3 @ce.
-@m_keyword{dmat2x3,GLSL dmat2x3,}
+@brief Double matrix with 3 columns and 1 row
+@m_since_latest
 */
-typedef Math::Matrix2x3<Double> Matrix2x3d;
+typedef Math::Matrix3x1<Double> Matrix3x1d;
 
 /**
 @brief Double matrix with 3 columns and 2 rows
@@ -1176,20 +1196,13 @@ Equivalent to GLSL @glsl dmat3x2 @ce.
 typedef Math::Matrix3x2<Double> Matrix3x2d;
 
 /**
-@brief Double matrix with 2 columns and 4 rows
-
-Equivalent to GLSL @glsl dmat2x4 @ce.
-@m_keyword{dmat2x4,GLSL dmat2x4,}
-*/
-typedef Math::Matrix2x4<Double> Matrix2x4d;
-
-/**
-@brief Double matrix with 4 columns and 2 rows
+@brief 3x3 double matrix
 
-Equivalent to GLSL @glsl dmat4x2 @ce.
-@m_keyword{dmat4x2,GLSL dmat4x2,}
+Equivalent to GLSL @glsl dmat3x3 @ce. Note that this is different from
+@ref Matrix3d, which contains additional functions for transformations in 2D.
+@m_keyword{dmat3x3,GLSL dmat3x3,}
 */
-typedef Math::Matrix4x2<Double> Matrix4x2d;
+typedef Math::Matrix3x3<Double> Matrix3x3d;
 
 /**
 @brief Double matrix with 3 columns and 4 rows
@@ -1199,6 +1212,20 @@ Equivalent to GLSL @glsl dmat3x4 @ce.
 */
 typedef Math::Matrix3x4<Double> Matrix3x4d;
 
+/**
+@brief Double matrix with 4 columns and 1 row
+@m_since_latest
+*/
+typedef Math::Matrix4x1<Double> Matrix4x1d;
+
+/**
+@brief Double matrix with 4 columns and 2 rows
+
+Equivalent to GLSL @glsl dmat4x2 @ce.
+@m_keyword{dmat4x2,GLSL dmat4x2,}
+*/
+typedef Math::Matrix4x2<Double> Matrix4x2d;
+
 /**
 @brief Double matrix with 4 columns and 3 rows
 
@@ -1207,6 +1234,15 @@ Equivalent to GLSL @glsl dmat4x3 @ce.
 */
 typedef Math::Matrix4x3<Double> Matrix4x3d;
 
+/**
+@brief 4x4 double matrix
+
+Equivalent to GLSL @glsl dmat4x4 @ce. Note that this is different from
+@ref Matrix4d, which contains additional functions for transformations in 3D.
+@m_keyword{dmat4x4,GLSL dmat4x4,}
+*/
+typedef Math::Matrix4x4<Double> Matrix4x4d;
+
 /** @brief Double two-dimensional quadratic Bézier curve */
 typedef Math::QuadraticBezier2D<Double> QuadraticBezier2Dd;
 

src/Magnum/Math/Math.h

@@ -67,11 +67,14 @@ template<class> class Matrix4;
 template<class> class Quaternion;
 
 template<std::size_t, std::size_t, class> class RectangularMatrix;
+template<class T> using Matrix2x1 = RectangularMatrix<2, 1, T>;
 template<class T> using Matrix2x3 = RectangularMatrix<2, 3, T>;
-template<class T> using Matrix3x2 = RectangularMatrix<3, 2, T>;
 template<class T> using Matrix2x4 = RectangularMatrix<2, 4, T>;
-template<class T> using Matrix4x2 = RectangularMatrix<4, 2, T>;
+template<class T> using Matrix3x1 = RectangularMatrix<3, 1, T>;
+template<class T> using Matrix3x2 = RectangularMatrix<3, 2, T>;
 template<class T> using Matrix3x4 = RectangularMatrix<3, 4, T>;
+template<class T> using Matrix4x1 = RectangularMatrix<4, 1, T>;
+template<class T> using Matrix4x2 = RectangularMatrix<4, 2, T>;
 template<class T> using Matrix4x3 = RectangularMatrix<4, 3, T>;
 
 template<template<class> class, class> class Unit;

src/Magnum/Math/RectangularMatrix.h

@@ -64,22 +64,25 @@ namespace Implementation {
 @tparam rows    Row count
 @tparam T       Underlying data type
 
-See @ref matrix-vector for brief introduction. See also @ref Matrix (square)
-and @ref Vector.
+See @ref matrix-vector for brief introduction. See also @ref Matrix (square),
+@ref Matrix3, @ref Matrix4 and @ref Vector.
 
 The data are stored in column-major order, to reflect that, all indices in
 math formulas are in reverse order (i.e. @f$ \boldsymbol A_{ji} @f$ instead
 of @f$ \boldsymbol A_{ij} @f$).
-@see @ref Matrix2x3, @ref Matrix3x2, @ref Matrix2x4, @ref Matrix4x2,
-    @ref Matrix3x4, @ref Matrix4x3, @ref Magnum::Matrix2x3,
-    @ref Magnum::Matrix2x3d, @ref Magnum::Matrix2x3h, @ref Magnum::Matrix2x3b,
-    @ref Magnum::Matrix2x3s, @ref Magnum::Matrix3x2, @ref Magnum::Matrix3x2d,
-    @ref Magnum::Matrix3x2h, @ref Magnum::Matrix3x2b, @ref Magnum::Matrix3x2s,
-    @ref Magnum::Matrix2x4, @ref Magnum::Matrix2x4d, @ref Magnum::Matrix2x4h,
-    @ref Magnum::Matrix2x4b, @ref Magnum::Matrix2x4s, @ref Magnum::Matrix4x2,
-    @ref Magnum::Matrix4x2d, @ref Magnum::Matrix4x2h, @ref Magnum::Matrix4x2b,
-    @ref Magnum::Matrix4x2s, @ref Magnum::Matrix3x4, @ref Magnum::Matrix3x4d,
-    @ref Magnum::Matrix3x4h, @ref Magnum::Matrix3x4b, @ref Magnum::Matrix3x4s,
+@see @ref Matrix2x1, @ref Matrix2x3, @ref Matrix2x4, @ref Matrix3x1,
+    @ref Matrix3x2, @ref Matrix3x4, @ref Matrix4x1, @ref Matrix4x2,
+    @ref Matrix4x3, @ref Magnum::Matrix2x1, @ref Magnum::Matrix2x1d,
+    @ref Magnum::Matrix2x3, @ref Magnum::Matrix2x3d, @ref Magnum::Matrix2x3h,
+    @ref Magnum::Matrix2x3b, @ref Magnum::Matrix2x3s, @ref Magnum::Matrix2x4,
+    @ref Magnum::Matrix2x4d, @ref Magnum::Matrix2x4h, @ref Magnum::Matrix2x4b,
+    @ref Magnum::Matrix2x4s, @ref Magnum::Matrix3x1, @ref Magnum::Matrix3x1d,
+    @ref Magnum::Matrix3x2, @ref Magnum::Matrix3x2d, @ref Magnum::Matrix3x2h,
+    @ref Magnum::Matrix3x2b, @ref Magnum::Matrix3x2s, @ref Magnum::Matrix3x4,
+    @ref Magnum::Matrix3x4d, @ref Magnum::Matrix3x4h, @ref Magnum::Matrix3x4b,
+    @ref Magnum::Matrix3x4s, @ref Magnum::Matrix4x1, @ref Magnum::Matrix4x1,
+    @ref Magnum::Matrix4x1d, @ref Magnum::Matrix4x2, @ref Magnum::Matrix4x2d,
+    @ref Magnum::Matrix4x2h, @ref Magnum::Matrix4x2b, @ref Magnum::Matrix4x2s,
     @ref Magnum::Matrix4x3, @ref Magnum::Matrix4x3d, @ref Magnum::Matrix4x3h,
     @ref Magnum::Matrix4x3b, @ref Magnum::Matrix4x3s
 */
@@ -501,10 +504,16 @@ template<std::size_t cols, std::size_t rows, class T> class RectangularMatrix {
         /**
          * @brief Multiply a vector
          *
-         * Internally the same as multiplying with one-column matrix, but
-         * returns vector. @f[
+         * Internally the same as multiplying with a one-column matrix, but
+         * returns a vector instead of a one-column matrix. @f[
          *      (\boldsymbol {Aa})_i = \sum_{k=0}^{m-1} \boldsymbol A_{ki} \boldsymbol a_k
          * @f]
+         *
+         * Vectors are treated as columns. An equivalent operation is
+         * multiplying a transposed matrix with an one-row matrix from the left
+         * side instead:
+         *
+         * @snippet Math.cpp RectangularMatrix-multiply-vector
          */
         Vector<rows, T> operator*(const Vector<cols, T>& other) const {
             return operator*(RectangularMatrix<1, cols, T>(other))[0];
@@ -606,27 +615,27 @@ template<std::size_t cols, std::size_t rows, class T> class RectangularMatrix {
 };
 
 /**
-@brief Matrix with 2 columns and 3 rows
+@brief Matrix with 2 columns and 1 row
+@m_since_latest
 
-Convenience alternative to @cpp RectangularMatrix<2, 3, T> @ce. See
-@ref RectangularMatrix for more information.
-@see @ref Magnum::Matrix2x3, @ref Magnum::Matrix2x3d, @ref Magnum::Matrix2x3h,
-    @ref Magnum::Matrix2x3b, @ref Magnum::Matrix2x3s
+Convenience alternative to @cpp RectangularMatrix<2, 1, T> @ce. See
+@ref RectangularMatrix for more information. There's no 1-column 2-row matrix typedef, use @ref Vector2 instead.
+@see @ref Magnum::Matrix2x1, @ref Magnum::Matrix2x1d
 */
 #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Multiple definitions still broken */
-template<class T> using Matrix2x3 = RectangularMatrix<2, 3, T>;
+template<class T> using Matrix2x1 = RectangularMatrix<2, 1, T>;
 #endif
 
 /**
-@brief Matrix with 3 columns and 2 rows
+@brief Matrix with 2 columns and 3 rows
 
-Convenience alternative to @cpp RectangularMatrix<3, 2, T> @ce. See
+Convenience alternative to @cpp RectangularMatrix<2, 3, T> @ce. See
 @ref RectangularMatrix for more information.
-@see @ref Magnum::Matrix3x2, @ref Magnum::Matrix3x2d, @ref Magnum::Matrix3x2h,
-    @ref Magnum::Matrix3x2b, @ref Magnum::Matrix3x2s
+@see @ref Magnum::Matrix2x3, @ref Magnum::Matrix2x3d, @ref Magnum::Matrix2x3h,
+    @ref Magnum::Matrix2x3b, @ref Magnum::Matrix2x3s
 */
 #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Multiple definitions still broken */
-template<class T> using Matrix3x2 = RectangularMatrix<3, 2, T>;
+template<class T> using Matrix2x3 = RectangularMatrix<2, 3, T>;
 #endif
 
 /**
@@ -642,15 +651,27 @@ template<class T> using Matrix2x4 = RectangularMatrix<2, 4, T>;
 #endif
 
 /**
-@brief Matrix with 4 columns and 2 rows
+@brief Matrix with 3 columns and 1 row
+@m_since_latest
 
-Convenience alternative to @cpp RectangularMatrix<4, 2, T> @ce. See
+Convenience alternative to @cpp RectangularMatrix<3, 1, T> @ce. See
+@ref RectangularMatrix for more information. There's no 1-column 3-row matrix typedef, use @ref Vector3 instead.
+@see @ref Magnum::Matrix3x1, @ref Magnum::Matrix3x1d
+*/
+#ifndef CORRADE_MSVC2015_COMPATIBILITY /* Multiple definitions still broken */
+template<class T> using Matrix3x1 = RectangularMatrix<3, 1, T>;
+#endif
+
+/**
+@brief Matrix with 3 columns and 2 rows
+
+Convenience alternative to @cpp RectangularMatrix<3, 2, T> @ce. See
 @ref RectangularMatrix for more information.
-@see @ref Magnum::Matrix4x2, @ref Magnum::Matrix4x2d, @ref Magnum::Matrix4x2h,
-    @ref Magnum::Matrix4x2b, @ref Magnum::Matrix4x2s
+@see @ref Magnum::Matrix3x2, @ref Magnum::Matrix3x2d, @ref Magnum::Matrix3x2h,
+    @ref Magnum::Matrix3x2b, @ref Magnum::Matrix3x2s
 */
 #ifndef CORRADE_MSVC2015_COMPATIBILITY /* Multiple definitions still broken */
-template<class T> using Matrix4x2 = RectangularMatrix<4, 2, T>;
+template<class T> using Matrix3x2 = RectangularMatrix<3, 2, T>;
 #endif
 
 /**
@@ -665,6 +686,30 @@ Convenience alternative to @cpp RectangularMatrix<3, 4, T> @ce. See
 template<class T> using Matrix3x4 = RectangularMatrix<3, 4, T>;
 #endif
 
+/**
+@brief Matrix with 4 columns and 1 row
+@m_since_latest
+
+Convenience alternative to @cpp RectangularMatrix<4, 1, T> @ce. See
+@ref RectangularMatrix for more information. There's no 1-column 4-row matrix typedef, use @ref Vector4 instead.
+@see @ref Magnum::Matrix4x1, @ref Magnum::Matrix4x1d
+*/
+#ifndef CORRADE_MSVC2015_COMPATIBILITY /* Multiple definitions still broken */
+template<class T> using Matrix4x1 = RectangularMatrix<4, 1, T>;
+#endif
+
+/**
+@brief Matrix with 4 columns and 2 rows
+
+Convenience alternative to @cpp RectangularMatrix<4, 2, T> @ce. See
+@ref RectangularMatrix for more information.
+@see @ref Magnum::Matrix4x2, @ref Magnum::Matrix4x2d, @ref Magnum::Matrix4x2h,
+    @ref Magnum::Matrix4x2b, @ref Magnum::Matrix4x2s
+*/
+#ifndef CORRADE_MSVC2015_COMPATIBILITY /* Multiple definitions still broken */
+template<class T> using Matrix4x2 = RectangularMatrix<4, 2, T>;
+#endif
+
 /**
 @brief Matrix with 4 columns and 3 rows
 

src/Magnum/Math/Test/RectangularMatrixTest.cpp

@@ -82,6 +82,7 @@ struct RectangularMatrixTest: TestSuite::Tester {
     void multiplyDivide();
     void multiply();
     void multiplyVector();
+    void multiplyRowVector();
 
     void transposed();
     void flippedCols();
@@ -115,8 +116,10 @@ typedef Vector<3, Float> Vector3;
 typedef Vector<2, Float> Vector2;
 using Magnum::BitVector3;
 
-typedef RectangularMatrix<4, 3, Int> Matrix4x3i;
-typedef RectangularMatrix<3, 4, Int> Matrix3x4i;
+typedef Math::Matrix3x1<Int> Matrix3x1i;
+typedef Math::Matrix4x1<Int> Matrix4x1i;
+typedef Math::Matrix4x3<Int> Matrix4x3i;
+typedef Math::Matrix3x4<Int> Matrix3x4i;
 typedef Vector<4, Int> Vector4i;
 typedef Vector<3, Int> Vector3i;
 typedef Vector<2, Int> Vector2i;
@@ -146,6 +149,7 @@ RectangularMatrixTest::RectangularMatrixTest() {
               &RectangularMatrixTest::multiplyDivide,
               &RectangularMatrixTest::multiply,
               &RectangularMatrixTest::multiplyVector,
+              &RectangularMatrixTest::multiplyRowVector,
 
               &RectangularMatrixTest::transposed,
               &RectangularMatrixTest::flippedCols,
@@ -606,6 +610,19 @@ void RectangularMatrixTest::multiplyVector() {
     /* There's no *= for vector and matrix multiplication either */
 }
 
+void RectangularMatrixTest::multiplyRowVector() {
+    /* Like multiplyVector() above, just transposed */
+
+    const Vector3i d{2, -2, 3};
+    const Matrix4x3i c{Vector3i{ 0,  1,  3},
+                       Vector3i{ 4,  5,  7},
+                       Vector3i{ 8,  9, 11},
+                       Vector3i{12, 13, 15}};
+    CORRADE_COMPARE(Matrix3x1i::fromVector(d)*c, (Matrix4x1i{
+       7, 19, 31, 43
+    }));
+}
+
 void RectangularMatrixTest::transposed() {
     Matrix4x3 original(Vector3( 0.0f,  1.0f,  3.0f),
                        Vector3( 4.0f,  5.0f,  7.0f),

src/Magnum/Math/Vector2.h

@@ -66,7 +66,8 @@ template<class T> inline T cross(const Vector2<T>& a, const Vector2<T>& b) {
 @brief Two-component vector
 @tparam T   Data type
 
-See @ref matrix-vector for brief introduction.
+See @ref matrix-vector for brief introduction. The vectors are columns, see
+@ref Matrix2x1 for a row vector.
 @see @ref Magnum::Vector2, @ref Magnum::Vector3h, @ref Magnum::Vector2d,
     @ref Magnum::Vector2ub, @ref Magnum::Vector2b, @ref Magnum::Vector2us,
     @ref Magnum::Vector2s, @ref Magnum::Vector2ui, @ref Magnum::Vector2i

src/Magnum/Math/Vector3.h

@@ -68,7 +68,8 @@ template<class T> inline Vector3<T> cross(const Vector3<T>& a, const Vector3<T>&
 @brief Three-component vector
 @tparam T   Data type
 
-See @ref matrix-vector for brief introduction.
+See @ref matrix-vector for brief introduction. The vectors are columns, see
+@ref Matrix3x1 for a row vector.
 @see @ref Magnum::Vector3, @ref Magnum::Vector3h, @ref Magnum::Vector3d,
     @ref Magnum::Vector3ub, @ref Magnum::Vector3b, @ref Magnum::Vector3us,
     @ref Magnum::Vector3s, @ref Magnum::Vector3ui, @ref Magnum::Vector3i

src/Magnum/Math/Vector4.h

@@ -41,7 +41,8 @@ namespace Magnum { namespace Math {
 @brief Four-component vector
 @tparam T   Data type
 
-See @ref matrix-vector for brief introduction.
+See @ref matrix-vector for brief introduction. The vectors are columns, see
+@ref Matrix4x1 for a row vector.
 @see @ref Magnum::Vector4, @ref Magnum::Vector4h, @ref Magnum::Vector4d,
     @ref Magnum::Vector4ub, @ref Magnum::Vector4b, @ref Magnum::Vector4us,
     @ref Magnum::Vector4s, @ref Magnum::Vector4ui, @ref Magnum::Vector4i