Positive Definite Matrices¶
Definition¶
A matrix \(A\) is positive definite if:
- \(A\) is symmetric (\(A = A^T\))
- For all non-zero vectors \(x\), the quadratic form \(x^TAx > 0\)
You can verify if a matrix is positive definite if its corresponding eigenvalues are positive.
Example¶
References¶
Second Derivative Test