AI engineering glossary · Linear algebra
What is orthogonal matrix?
Orthogonal matrix: A square matrix whose columns are mutually perpendicular unit vectors, so its transpose is also its inverse. Multiplying by it rotates or reflects vectors without changing their lengths or angles.
Orthogonal matrix: an example
A 2-D rotation by 90 degrees, [[0,-1],[1,0]], is orthogonal: it turns [1, 0] into [0, 1] and both have length 1.
Related terms
More Linear algebra terms
- Orthogonal projection
- Orthogonal vectors
- Orthonormal basis
- Outer product
- Permutation matrix
- Pivot
- Positive definite matrix
- Positive semi-definite matrix
Where you learn it
Orthogonal 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.