List questions from matrix-equations

619

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Let $v,w \in R^n$ with $||u||=||w||=1$. Prove that there exists orthogonal matrix $A$ such that $Av=w$.

Published on 26 Mar 2026 - 22:55

120

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Prove that $(A+BB^T)^{-1}B=A^{-1}B(I+B^TA^{-1}B)^{-1}$

Published on 31 Mar 2026 - 12:16

97

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Simplify Matrices and Vector Multiplication

Published on 30 Mar 2026 - 13:34

50

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Given the equation $8CC^T=2I_4$, deduce $C^{-1}$

Published on 24 Oct 2019 - 19:20

204

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Find all matrices $A\in \mathbb{R}^{2\times2}$ such that $A^2=\bf{0}$

Published on 25 Mar 2026 - 21:01

30

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The detection value $(A^2 + A) $ is:

Published on 28 Oct 2019 - 19:52

142

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Expressing the solution to a quadratic matrix equation

Published on 29 Oct 2019 - 14:14

405

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Matrix Transpose Reordering

Published on 29 Oct 2019 - 20:01

103

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Finding solution to $Xa=b$ where $X$ has to be symmetric positive-definite

Published on 29 Mar 2026 - 23:25

165

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Characteristic Polynomial on 3 by 3 matrix

Published on 30 Oct 2019 - 16:39

51

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How to prove this identity involving traces of resolvents?

Published on 28 Mar 2026 - 5:23

74

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Let the eigen values of $A$ be distinct, $A=P\Lambda P^{-1}$ and $A^{T}=Q\Lambda Q^{-1}$,show that $Q^{T}P=I$

Published on 31 Oct 2019 - 18:10

21

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Matrix Equation Inverse

Published on 02 Nov 2019 - 13:12

30

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Is it possible to find a vector $x$ such that for diagonal matrix $D$, $xx^T+D$ has a displacement structure?

Published on 02 Nov 2019 - 23:06

388

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Matrix Equation with factoring

Published on 02 Nov 2019 - 23:16

List Question

Let $v,w \in R^n$ with $||u||=||w||=1$. Prove that there exists orthogonal matrix $A$ such that $Av=w$.

Prove that $(A+BB^T)^{-1}B=A^{-1}B(I+B^TA^{-1}B)^{-1}$

Simplify Matrices and Vector Multiplication

Given the equation $8CC^T=2I_4$, deduce $C^{-1}$

Find all matrices $A\in \mathbb{R}^{2\times2}$ such that $A^2=\bf{0}$

The detection value $(A^2 + A) $ is:

Expressing the solution to a quadratic matrix equation

Matrix Transpose Reordering

Finding solution to $Xa=b$ where $X$ has to be symmetric positive-definite

Characteristic Polynomial on 3 by 3 matrix

How to prove this identity involving traces of resolvents?

Let the eigen values of $A$ be distinct, $A=P\Lambda P^{-1}$ and $A^{T}=Q\Lambda Q^{-1}$,show that $Q^{T}P=I$

Matrix Equation Inverse

Is it possible to find a vector $x$ such that for diagonal matrix $D$, $xx^T+D$ has a displacement structure?

Matrix Equation with factoring

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