List questions from eigenvalues-eigenvectors

Published on 01 Jun 2018 - 6:24

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Find the eigenvalues of the block matrix

Published on 01 Jun 2018 - 6:49

199

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IVP Differential Equation

Published on 01 Jun 2018 - 7:49

50

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Find a positive-definite scalar product for which $F:\mathbb{R^3}\to \mathbb{R^3}$ is symmetrical

Published on 25 Mar 2026 - 6:30

59

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A block-wise eigenvalue problem

Published on 01 Jun 2018 - 17:17

65

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Simple Eigenspace Calculation

Published on 01 Jun 2018 - 18:32

218

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Prove that $\operatorname{span}(\{x ∈ V: x $ is an eigenvector of $T\}) = E_{λ_1} ⊕ E_{λ_2} ⊕· · ·⊕E_{λ_k}.$

Published on 26 Mar 2026 - 12:36

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Show That Minimizer of Rayleigh Quotient Is the Smallest Eigenvalue - $ \min_{x : \left\| x \right\| = 1} {x}^{} {A}^{} A x = {\lambda}_{1}^{2} $

Published on 29 Mar 2026 - 3:35

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Finding eigenvalues and there properties of permutation matrix

Published on 25 Mar 2026 - 21:12

90

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Too many eigenvalues?

Published on 26 Mar 2026 - 8:03

1.1k

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Any non-trivial $T$-invariant subspace of $V$ contains an eigenvector of $T.$

Published on 25 Mar 2026 - 6:13

416

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Why eigenvalues of a symmetric matrix with zero row sum are not affected with this special manipulation?

Published on 22 Mar 2026 - 18:21

43

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Can you find the result of a linear transformation by projecting a given vector onto known eigenvectors?

Published on 03 Jun 2018 - 22:47

223

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Eigenvalue of higher rank tensor

Published on 04 Jun 2018 - 3:20

445

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Prove that for any eigenvalue, its eigenspace is in direct sum with the sum of all other eigenspaces of distinct eigenvlaues.

Published on 28 Mar 2026 - 21:34

List Question

Let $A∈M_n$ ($\mathbb R$). If $A^2=-I$ then,

Find the eigenvalues of the block matrix

IVP Differential Equation

Find a positive-definite scalar product for which $F:\mathbb{R^3}\to \mathbb{R^3}$ is symmetrical

A block-wise eigenvalue problem

Simple Eigenspace Calculation

Prove that $\operatorname{span}(\{x ∈ V: x $ is an eigenvector of $T\}) = E_{λ_1} ⊕ E_{λ_2} ⊕· · ·⊕E_{λ_k}.$

Show That Minimizer of Rayleigh Quotient Is the Smallest Eigenvalue - $ \min_{x : \left\| x \right\| = 1} {x}^{} {A}^{} A x = {\lambda}_{1}^{2} $

Finding eigenvalues and there properties of permutation matrix

Too many eigenvalues?

Any non-trivial $T$-invariant subspace of $V$ contains an eigenvector of $T.$

Why eigenvalues of a symmetric matrix with zero row sum are not affected with this special manipulation?

Can you find the result of a linear transformation by projecting a given vector onto known eigenvectors?

Eigenvalue of higher rank tensor

Prove that for any eigenvalue, its eigenspace is in direct sum with the sum of all other eigenspaces of distinct eigenvlaues.

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