Prove that $a$ is an eigen value of $p(T)$ where $T$ is a linear operator on $V$ $\iff$ $a=p(\lambda$ )
112900
Eigenvalue of a polynomial evaluated in a operator
3682
If $V = \text{null}(\textsf{T}-\lambda\textsf{I}) \oplus \text{range}(\textsf{T}-\lambda\textsf{I})$, then prove that $\textsf{T}$ is diagonalizable
153432
Question on the proof of the spectral mapping theorem for polynomials
4509
Proof that an involutory matrix has eigenvalues 1,-1
112024
Let $T:V → V$ be a linear transformation where $V$ is finite dimensional.
35013
Demonstration: If all vectors of $V$ are eigenvectors of $T$, then there is one $\lambda$ such that $T(v) = \lambda v$ for all $v \in V$.
98323
If A is invertible, prove that $\lambda \neq 0$, and $\vec{v}$ is also an eigenvector for $A^{-1}$, what is the corresponding eigenvalue?
153448
Show that $A\in\mathbb{C}_n$ is normal $\iff$ $tr(A*A) = \sum_{i = 1}^n|\lambda_i|^2$, where $\lambda_1,...,\lambda_n$ are the eigenvalues of $A$.
36567
$A^{T}A$ positive definite then A is invertible?
47829
Prove that $\operatorname{trace}(A^TA) = 0\ \iff\ A = 0$.
80346
If every eigenvector of $T$ is also an eigenvector of $T^{*}$ then $T$ is a normal operator
56083
Find the eigenvalues of a projection operator
141628
How did the equation $|A- \lambda I| = 0$ came for finding Eigen values of a Matrix
104293
How to prove "eigenvalues of polynomial of matrix $A$ = polynomial of eigenvalues of matrix $A$ "
88971
An approximate eigenvalue for $ T \in B(X) $.
104036
Right eigenvector λ and left eigenvector are orthogonal.
88473
Proof that the trace of a matrix is the sum of its eigenvalues