List questions from matrices

Published on 03 May 2018 - 23:01

121

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How tot prove the inequality: $\lambda_{min}(S^TS)\lambda_k(A)\le\lambda(S^TAS)\le\lambda_{max}(S^TS)\lambda_k(A)$

Published on 10 Apr 2026 - 10:20

49

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$\forall A,B \in M_n(\mathbb F),AB=BA,\exists C \in M_n(\mathbb F),f(x),g(x)\in \mathbb F[x],A=f(C),B=g(C)?$

Published on 04 May 2018 - 5:38

394

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Matrix with integer entries, first row as $(1~2~3~\cdots~n)$, and determinant $k$

Published on 04 May 2018 - 5:51

1.2k

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A totally unimodular matrix

Published on 09 Apr 2026 - 13:51

527

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Describe the finite order integer matrices over complex field

Published on 25 Mar 2026 - 10:58

439

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Quaternion - Conjugate

Published on 11 Apr 2026 - 0:14

3.8k

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Product rule for vector-valued functions

Published on 25 Mar 2026 - 12:30

382

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Stable way to find QR-decomposition

Published on 08 Apr 2026 - 23:09

432

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How many square roots can a complex matrix with distinct non zero eigenvalues can take?

Published on 25 Mar 2026 - 3:18

86

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What are the eigenvalues of $f(X) = AX + CXB$ if the eigenvalues of $A$, $B$ and $C$ are known?

Published on 11 Apr 2026 - 19:07

1k

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Simple proof that if $A^n=I$ then $\mathrm{tr}(A^{-1})=\overline{\mathrm{tr}(A)}$

Published on 11 Apr 2026 - 6:31

124

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Any matrix ring $R_k$ is isomorphic to a subring of the ring $R_{2^k}$

Published on 25 Mar 2026 - 3:03

74

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Transpose of the matrix of a linear map

Published on 12 Apr 2026 - 1:32

115

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Linear System with rank deficiency

Published on 29 Mar 2026 - 14:57

List Question

Show that $\operatorname{rank}(A)=\operatorname{rank}(B)$

How tot prove the inequality: $\lambda_{min}(S^TS)\lambda_k(A)\le\lambda(S^TAS)\le\lambda_{max}(S^TS)\lambda_k(A)$

$\forall A,B \in M_n(\mathbb F),AB=BA,\exists C \in M_n(\mathbb F),f(x),g(x)\in \mathbb F[x],A=f(C),B=g(C)?$

Matrix with integer entries, first row as $(1~2~3~\cdots~n)$, and determinant $k$

A totally unimodular matrix

Describe the finite order integer matrices over complex field

Quaternion - Conjugate

Product rule for vector-valued functions

Stable way to find QR-decomposition

How many square roots can a complex matrix with distinct non zero eigenvalues can take?

What are the eigenvalues of $f(X) = AX + CXB$ if the eigenvalues of $A$, $B$ and $C$ are known?

Simple proof that if $A^n=I$ then $\mathrm{tr}(A^{-1})=\overline{\mathrm{tr}(A)}$

Any matrix ring $R_k$ is isomorphic to a subring of the ring $R_{2^k}$

Transpose of the matrix of a linear map

Linear System with rank deficiency

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