A matrix is positive if and only if it is Hermitian and its eigenvalues are positive
30268
Positive definite matrix must be Hermitian
73807
Prove positive definiteness
85550
Positive definiteness of difference of inverse matrices
61931
Positive operator is bounded
153127
Is $U=V$ in the SVD of a symmetric positive semidefinite matrix?
36771
How to prove that A is normal if and only if there's a unitary matrix V,s.t. A*=AV?
118417
Is $AA^T$ positive semidefinite?
114208
Does non-symmetric positive definite matrix have positive eigenvalues?
140252
Matrices - Conditions for $AB+BA=0$
30882
Proving Invertibility and Eigenvalues
20309
Product and sum of positive operators is positive
86940
Proving an inequality in Eigenvalues of a matrix
94424
Matrices and Eigenvalues of Norm
24454
The relationship between the eigenvalues of matrices $XY$ and $YX$
135316
A basic question on diagonalizability of a matrix
44652
Minimum and Maximum eigenvalue inequality from a positive definite matrix.
36775
Matrix semi-positive definite