matrix multiplication


Summary

Non-commutative

  • multiply A by B vs multiply B to A
  • pre-multiply vs post-multiply

unless they are diagonal matrices

Rules

zero product -> product of two nonzero matrices can be 0

Block multiplication

  • spread the multiplication to columns/rows
  • rows of first, cols of second

Concept

Matrix multiplication

matrix_mul.png

Size of matrices for the product to be well defined

Multiplication of diagonal matrices is commutative

Power of square matrices

Application

Row vector and column vector

Using the rules of matrix multiplication

Finding a specific column using block multiplication

Extra

Octave

octave
# Matrix multiplication
A * A