If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
30923
Is the matrix $A^*A$ and $AA^*$ hermitian?
136643
Continuity of eigenvalues and spectral radius for a general matrix
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
98135
Show that the determinant of $A$ is equal to the product of its eigenvalues
121253
Prove that any complex matrix can be expressed in term of Hermitian and anti-Hermitian matrices
94424
Matrices and Eigenvalues of Norm
54099
What are the eigenvalues of $\operatorname{ad}x$?
80022
Eigenvector of A by $A^2$
33477
Proving that if $A$ is a $8\times 8$ matrix over $\mathbb{R}$ and $A^3=A$, then $A$ is diagonalizable.
135171
Under what conditions is the difference between a rank $1$, postive semidefinite matrix and a hermitian matrix positive semidefinite?
100731
Positive operator has a positive spectrum?
38635
How to prove that the matrix $A^k$ approaches $0$ as $k$ approaches infinity
75211
Theorem about positive matrices
28584
Eigenvalues and eigenspaces of AB
140252
Matrices - Conditions for $AB+BA=0$
5058
Eigenvalues of the rank one matrix $uv^T$
78298
On the nilpotence of the matrix $AB-BA$