Positive definite matrices and positive semi-definite matrices.

Some authors do not require positive definite matrices to be a subclass of Hermitian matrices, only that the symmetric/Hertian part of the matrix be positive definite.


Thm: 7.2.5; Thm: 7.2.6; Cor: 7.2.7;

Cholesky factorization (p. 114): For any positive definite matrix B, there exists a lower triangular matrix L with nonnegative diagonal entries, such that $B = L L^*$. If B is positive definite, then L is unique.

🏷 Category=Algebra Category=Matrix Analysis