value + matrix, adds a value to all matrix components

matrix + value, adds a value to all matrix components

matrix + matrix, adds the values of two matrices component wise

value / matrix, divides a value by all matrix components

matrix / value, divides all matrix components with a value

! matrix, calculates the inverse of the matrix optimized 4x4 matrix inversion using cramer's rule, found in the game engine http://www.ogre3d.org takes about 1,8ns to execute on intel core2 duo 2Ghz, the intel reference implementation (not assembly optimized) was about 2,2ns. http://www.intel.com/design/pentiumiii/sml/24504301.pdf

value * matrix, multiplies all matrix components with a value

matrix * value, multiplies all matrix components with a value

matrix * matrix, performs a matrix multiplication

matrix * 2d vector, applies a matrix transform to a 2d-vector, (x, y, 0, 1)

matrix * 3d vector, applies a matrix transform to a 3d-vector, (x, y, z, 1) and divides by w

matrix * 4d vector, applies a matrix transform to a 4d-vector

~ matrix, calculates the determinant of the matrix

value - matrix, subtracts all matrix components from a value

matrix - value, subtracts a value from all matrix components

matrix - matrix, subtracts the components of B from the components of A

- matrix, flips the sign off all matrix components

+ matrix, makes no changes to a matrix