AI engineering glossary · Linear algebra
What is positive definite matrix?
Positive definite matrix: A symmetric matrix A for which x^T A x is greater than zero for every non-zero vector x; equivalently all its eigenvalues are positive. It describes a bowl-shaped surface with a single minimum and can be inverted.
Positive definite matrix: an example
[[2,0],[0,3]] is positive definite: x^T A x = 2*x1^2 + 3*x2^2 is positive unless x is the zero vector.
Related terms
More Linear algebra terms
- Positive semi-definite matrix
- Power iteration
- Projection
- Projection matrix
- Pseudoinverse
- QR decomposition
- Quadratic form
- Rank
Where you learn it
Positive 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.