BitWithBiteAI & Machine Learning · Quick Reference
Matrix Operations: Multiplication, Transpose & Inverse Cheat Sheet
In one line: Matrix multiplication is not what most people guess on first encounter (multiplying each matching position together, like you would with two vectors). It's a different, specific...
Key Ideas
1Matrix Multiplication — The Rule That Trips Everyone Up Once. Matrix multiplication is not what most people guess on first encounter (multiplying each matching position together, like you would with two vectors). It's a different...
2A Worked Example. Take a small 2×2 matrix A and a 2×1 vector b (a vector is just a matrix with one column):
3The Transpose. The transpose flips a matrix over its diagonal — rows become columns, columns become rows. Written as AT.
4The Inverse — Intuition Over Computation. For regular numbers, the inverse of 5 is 1/5, because 5 × (1/5) = 1. Matrices have a similar idea: the inverse of matrix A, written A−1, is the matrix that...
Code Examples
A = [ 1 2 ] b = [ 5 ]
[ 3 4 ] [ 6 ]
A × b = [ (1×5 + 2×6) ] = [ 17 ]
[ (3×5 + 4×6) ] [ 39 ]
A = [ 1 2 3 ] Aᵀ = [ 1 4 ]
[ 4 5 6 ] [ 2 5 ]
[ 3 6 ]