Special Matrices
Identity Matrix
The identity matrix multiplied by matrix A returns matrix A.
This matrix is simply a diagonal line of 1s in a matrix of 0s.
┌ ┐ │ 1 0 0│ │ 0 1 0│ │ 0 0 1│ └ ┘
Permutation Matrices
A permutation matrix multiplied by matrix A returns a row-exchanged transformation of A.
┌ ┐┌ ┐ ┌ ┐ │ 0 1││ 1 2│ │ 3 4│ │ 1 0││ 3 4│=│ 1 2│ └ ┘└ ┘ └ ┘
See Permutation Matrices for more information.
Inverse Matrices
An inverse matrix A-1 multiplied by matrix A returns the identity matrix.
If A-1 exists, then A is invertible and non-singular. Not all matrices are invertible.
See Matrix Inversion for more information.
Symmetric Matrices
A symmetric matrix is any matrix that is equal to its transpose.
┌ ┐ │ 1 7│ │ 7 2│ └ ┘
See Symmetric Matrices for more information.