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│
└      ┘

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.

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.

A symmetric matrix is any matrix that is equal to its transpose.

┌    ┐
│ 1 7│
│ 7 2│
└    ┘

See Symmetric Matrices for more information.