TIL of the Identity Matrix permalink

Today I learned of the identity matrix in Andrew Ng’s Machine Learning class on Coursera! Identity matrices are a class of matrix that have special properties:

• they are square - meaning, they’re always n x n where n is both the count of rows and the count of columns (e.g. 1x1, 2x2, 3x3)
• they have all 1s across the diagonal of the matrix
• they have all 0s everywhere else

For example:

1 0 0 0
0 1 0 0
0 0 1 0
0 0 0 1

(I need to figure out if Github Pages supports LaTeX or other math syntax!)

When multiplied against other matrices, they act in the same way as multiplying a number (z) times 1:

z * 1 = 1 * z = z

Substituting our matrix:

A * I = I * A = A

This does not mean the multiplication is commutative. If A = R^3x2 that means, depending on matrix order, I = R^2x2 or I = R^3x3.