Prove that $A$ and $A^t$ have the same eigenvalues.
50384
A matrix and its transpose have the same set of eigenvalues/other version: $A$ and $A^T$ have the same spectrum
128453
If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable
30882
Proving Invertibility and Eigenvalues
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
80544
Need verification - Prove a Hermitian matrix $(\textbf{A}^\ast = \textbf{A})$ has only real eigenvalues
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
129977
Prove that $\lambda_1^2$, $\lambda_1\lambda_2$ and $\lambda_2^2$ are eigenvalues of matrix $A$
50417
Prove that the triangles $ABC$ and $AB^{'}C^{'}$ have the same incentre.
28003
How to prove $A+ A^T$ symmetric, $A-A^T$ skew-symmetric.
86940
Proving an inequality in Eigenvalues of a matrix
80346
If every eigenvector of $T$ is also an eigenvector of $T^{*}$ then $T$ is a normal operator
149923
eigenvalues of A - aI in terms of eigenvalues of A
60723
Prove that if $A$ is normal, then eigenvectors corresponding to distinct eigenvalues are necessarily orthogonal (alternative proof)
30665
Elegant proofs that similar matrices have the same characteristic polynomial?
106288
Prove that the eigenvalues of a block matrix are the combined eigenvalues of its blocks
19132
Similar matrices have the same eigenvalues with the same geometric multiplicity
155828
How do I show that $A$ and $A^T$ are similar, given that the minimal polynomial of $A$ splits over $\mathbb{F}$?