AI engineering glossary · Linear algebra
What is Gram-Schmidt process?
Gram-Schmidt process: A procedure that turns a list of independent vectors into an orthonormal list spanning the same space: take each vector, subtract its projections onto those already processed, and scale the remainder to length 1. It underlies QR decomposition.
Gram-Schmidt process: an example
From [1, 1] and [1, 0], the first becomes [0.707, 0.707]; subtracting its projection from [1, 0] and normalising gives [0.707, -0.707].
Related terms
More Linear algebra terms
- Hadamard product
- Homogeneous coordinates
- Hyperplane
- Identity matrix
- Ill-conditioned matrix
- Infinity norm
- Inner product
- Inverse matrix
Where you learn it
Gram-Schmidt process is part of the AI Engineering Program, which teaches it with notes, a hands-on lab and an exam. The first lesson is free.