Why are eigenvalues of nilpotent matrices equal to zero?
10001
Prove that the only eigenvalue of a nilpotent operator is 0?
34183
An equivalent condition with $\{0\}$ being the only nilpotent ideal
149981
Find the eigenvalues and eigenvectors with zeroes on the diagonal and ones everywhere else.
74441
Zero divisors in matrix rings
133758
Traces of powers of a matrix $A$ over an algebra are zero implies $A$ nilpotent.
130268
How to prove that a nilpotent matrix is not invertible?
22222
Properties of zero-diagonal symmetric matrices
19649
A question about the proof of "a symmetric matrix has real eigenvalues".
52621
Why is $\det(A - \lambda I)$ zero?
149916
Minimum eigenvalue and singular value of a square matrix
41932
Prove that $\lambda = 0$ is an eigenvalue if and only if A is singular.
128043
$A^n=0$ for $A$ nilpotent without the use of minimal polynomial
21571
Why are real symmetric matrices diagonalizable?
42799
Let $x$ and $y$ be two non-zero $n × 1$ vectors. If $y^T$ denotes the transpose of $y$, what are the eigenvalues of the $n × n$ matrix $xy^T$
18939
Eigenvalues of the transpose
125569
Prove that the eigenvalues of a real symmetric matrix are real
70455
Why are all nonzero eigenvalues of the skew-symmetric real matrices pure imaginary?