AI engineering glossary · Linear algebra
What is positive semi-definite matrix?
Positive semi-definite matrix (also called PSD matrix): A symmetric matrix A for which x^T A x is never negative, so all eigenvalues are zero or positive. Covariance matrices and kernel matrices always have this property, and it marks a valid, non-negative measure of spread.
Positive semi-definite matrix: an example
The covariance matrix [[1,1],[1,1]] of two identical features is positive semi-definite, with eigenvalues 2 and 0.
Related terms
More Linear algebra terms
- Power iteration
- Projection
- Projection matrix
- Pseudoinverse
- QR decomposition
- Quadratic form
- Rank
- Rank-nullity theorem
Where you learn it
Positive semi-definite 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.