Prove that the set of eigenvalues of block matrix with blocks $A$ and $B$ is the union of eigenvalues of $A$ and $B$.
106288
Prove that the eigenvalues of a block matrix are the combined eigenvalues of its blocks
54740
Proofs of Determinants of Block matrices
72326
Determinant of block matrix with commuting blocks
116539
Eigenvalues of matrix satisfying $A^2 = A$
88473
Proof that the trace of a matrix is the sum of its eigenvalues
19649
A question about the proof of "a symmetric matrix has real eigenvalues".
110086
Let $A$ be an $m \times n$ matrix. Show $A^TA$ and $AA^T$ have the same eigenvalues
8920
There exists $C\neq0$ with $CA=BC$ iff $A$ and $B$ have a common eigenvalue
94424
Matrices and Eigenvalues of Norm
119387
If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
7457
Prove that $J^+AJ$ has positive eigenvalues
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
149287
Prove that $A,B>0$ and $A_{ij}0$
80876
Proof of $A\cap(B\cup C) = (A\cap B)\cup(A\cap C)$
126337
Eigenvalues in orthogonal matrices
75966
Prove that if $A$ is a set with $m$ elements, $B$ is a set with $n$ elements, and $A \cap B = \emptyset$, then $A \cup B$ has $m+n$ elements.
26570
Prove $\operatorname{rank}(AB) = \operatorname{rank}(B)$