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| * The [[LinearAlgebra/Determinants|determinant]] is positive, and all subdeterminants are also positive. | * The [[LinearAlgebra/Determinant|determinant]] is positive, and all subdeterminants are also positive. |
Positive Definiteness
A matrix is positive definite if all eigenvalues are positive. A matrix is positive semi-definite if all eigenvalues are positive or zero.
Contents
Description
A positive definite matrix, by definition, has the property that all eigenvalues are positive. Beyond this:
A positive definite matrix is also symmetric.
- All pivots are positive.
The determinant is positive, and all subdeterminants are also positive.
'Semi-definite' is a slight modification, allowing 0.