AI engineering glossary · Linear algebra
What is projection matrix?
Projection matrix (also called Hat matrix): A matrix P that performs a projection when it multiplies a vector, satisfying P times P equals P because projecting twice changes nothing. For projection onto the columns of X it equals X (X^T X)^-1 X^T, the 'hat matrix' of regression.
Projection matrix: an example
P = [[1,0],[0,0]] projects any 2-D vector onto the x-axis: P [3, 4] = [3, 0].
Related terms
- Projection
- Least squares
- Idempotent matrix
- Design matrix
More Linear algebra terms
- Pseudoinverse
- QR decomposition
- Quadratic form
- Rank
- Rank-nullity theorem
- Rank-one matrix
- Reduced row echelon form
- Rotation matrix
Where you learn it
Projection matrix is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.