Show that the eigenvalues of $T^*T$ and $TT^*$ are the same for a linear operator $T$ on finite dimensional space.
88349
Are the eigenvalues of $AB$ equal to the eigenvalues of $BA$? (Citation needed!)
71040
If $ \operatorname{Tr}(M^k) = \operatorname{Tr}(N^k)\;\forall 1\leq k \leq n$, then how do we show the $M$ and $N$ have the same eigenvalues?
6514
Prove $T$ has at most two distinct eigenvalues
126337
Eigenvalues in orthogonal matrices
128453
If $A$ has two eigenvalues $\lambda _1, \lambda_2$ and $\dim (E_{\lambda_1})=n-1$, then $A$ is diagonalizable
103839
Proving that $T^{2} = T$ for a linear operator on $W$ implies that $V = \operatorname{Null} T \oplus \operatorname{Range} T$
119387
If $A$ is any matrix then $A^*A$ and $AA^*$ are Hermitian with non-negative eigenvalues
150228
If $E$ has eigenvalues $\lambda_1, \ldots, \lambda_n$, then $B \mapsto [E,B] = EB - BE$ has eigenvalues $\lambda_i - \lambda_j$.
134981
Eigenvalues of $L^\dagger L$ are positive
88971
An approximate eigenvalue for $ T \in B(X) $.
92744
These two operators commute...but their eigenvectors aren't all the same. Why?
28584
Eigenvalues and eigenspaces of AB
55377
Non-zero eigenvalues of $AA^T$ and $A^TA$
129549
Showing that the orthogonal projection in a Hilbert space is compact iff the subspace is finite dimensional
56943
Normal operator with real spectrum is hermitian.
137890
Diagonalizable Operators and characteristic polynomials
135420
Determining eigenvalues, eigenvectors of $A\in \mathbb{R}^{n\times n}(n\geq 2)$.