List questions from eigenvalues-eigenvectors

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$\exists\alpha\in\mathbf{F}(|\alpha-\lambda|<\frac{1}{1000}\ \text{and}\ T-\alpha I \ \text{is}\ \text{invertible})$

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Prove that $|\phi|^2 = \lambda$, where $\lambda$ is the largest eigenvalue of the selfadjoint mapping $\bar \phi \circ \phi$.

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Prove $T(Aut(\lambda))\subset Aut(\lambda)$ where $A\in Mat_n(\mathbb{K})$ and $\lambda$ eigenvalue of $A$

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number of matrices with max eignevalue greater than determinant

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List Question

Prove/disprove that $A = kI$

Spectrum of cocktail party graph?

$\exists\alpha\in\mathbf{F}(|\alpha-\lambda|<\frac{1}{1000}\ \text{and}\ T-\alpha I \ \text{is}\ \text{invertible})$

Prove that $|\phi|^2 = \lambda$, where $\lambda$ is the largest eigenvalue of the selfadjoint mapping $\bar \phi \circ \phi$.

Eigen values of a nilpotent matrix over a finite field?

Prove $T(Aut(\lambda))\subset Aut(\lambda)$ where $A\in Mat_n(\mathbb{K})$ and $\lambda$ eigenvalue of $A$

Can diagonally dominant matrix be written as the sum of diagonally dominant matrices?

Factorization of Normal Operator

An example of non-similar matrices with same eigenvalues, rank and determinant

Zolotarev number and commuting matrices

Root of upper triangular matrices

Friedberg linear algebra theorem 5.9

Symbolic Math in a Computer Algebra System

Characteristic polynomial of matrix with real coefficients

number of matrices with max eignevalue greater than determinant

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