every symmetric matrix has at least one real eigenvalue
127799
Eigenvalues of symmetric matrices are real without (!) complex numbers
144898
Let $A$ be complex matrix and $x$ be eigenvalue of $A\overline{A}$. Algebraic multiplicity of $x$ is even.
110200
Determinant of a Special Symmetric Matrix
72046
Prove all eigenvalues of $A^*A$ are non-negative
98656
Geometric multiplicity of the largest eigenvalue
27778
Eigenvalues of a real skew symmetric matrix
15417
Tricky problem on skew-symmetric matrices
136643
Continuity of eigenvalues and spectral radius for a general matrix
114208
Does non-symmetric positive definite matrix have positive eigenvalues?
94424
Matrices and Eigenvalues of Norm
158724
Show that $B$ is diagonalizable if If $AB=BA$ and $A$ has distinct real eigenvalues
120937
Matrices that commute with all matrices
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
149923
eigenvalues of A - aI in terms of eigenvalues of A
88473
Proof that the trace of a matrix is the sum of its eigenvalues
98541
If a Matrix Has Only Zero as an Eigen-Value Then It Is Nilpotent
81176
A normal matrix with real eigenvalues is Hermitian