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
wheren
is both the count of rows and the count of columns (e.g. 1x1, 2x2, 3x3) - they have all
1
s across the diagonal of the matrix - they have all
0
s 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
.