List questions from companion-matrices

Published on 13 May 2021 - 18:17

49

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Companion matrix of matrix valued polynomial coefficients

Published on 24 Jun 2021 - 13:12

63

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Existence of a real $4 \times 4$ matrix satisfying the equation $x^2+1=0$.

Published on 08 Jul 2021 - 16:03

69

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Solving a general ODE

Published on 13 Jul 2021 - 11:24

203

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Determinant of sort of companion matrix

Published on 24 Oct 2021 - 20:22

29

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Generating synthetic multivariate time series with stable VAR model

Published on 23 Feb 2026 - 2:54

66

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Let $f \in \mathbb{F}[x]$ and $A_f=c(f) $ be the companion matrix of $f$. Given $ g \in \mathbb{F}[x] $ show that $ \dim \ker g(A_f) \leq \deg g $.

Published on 02 Dec 2021 - 14:47

159

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Companion matrices over the Galois field with two elements

Published on 05 Dec 2021 - 1:44

130

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Converting a monic polynomial of degree $n$ to its companion matrix

Published on 31 Jan 2022 - 17:22

137

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If $b$ is a cyclic vector, what is significant about $\begin{bmatrix} A - \lambda I & b \end{bmatrix}$?

Published on 23 Feb 2026 - 9:45

538

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minimal and characteristic polynomial of this operator

Published on 05 May 2022 - 9:53

101

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Comparing values and signs of determinant of companion matrices.

Published on 27 Jul 2022 - 5:02

84

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Characteristic polynomial of A and -A (where A is a companion matrix)

Published on 28 Jul 2022 - 18:20

224

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Companion matrix must have one Jordan block per eigenvalue: recurrence sequence perspective

Published on 29 Oct 2022 - 4:26

56

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How to calculate the eigenvalues of $A^\ast A$ where $A$ is a companion matrix?

Published on 06 Nov 2022 - 12:17

List Question

Characteristic polynomials of powers of a companion matrix in terms of coefficients.

Companion matrix of matrix valued polynomial coefficients

Existence of a real $4 \times 4$ matrix satisfying the equation $x^2+1=0$.

Solving a general ODE

Determinant of sort of companion matrix

Generating synthetic multivariate time series with stable VAR model

Let $f \in \mathbb{F}[x]$ and $A_f=c(f) $ be the companion matrix of $f$. Given $ g \in \mathbb{F}[x] $ show that $ \dim \ker g(A_f) \leq \deg g $.

Companion matrices over the Galois field with two elements

Converting a monic polynomial of degree $n$ to its companion matrix

If $b$ is a cyclic vector, what is significant about $\begin{bmatrix} A - \lambda I & b \end{bmatrix}$?

minimal and characteristic polynomial of this operator

Comparing values and signs of determinant of companion matrices.

Characteristic polynomial of A and -A (where A is a companion matrix)

Companion matrix must have one Jordan block per eigenvalue: recurrence sequence perspective

How to calculate the eigenvalues of $A^\ast A$ where $A$ is a companion matrix?

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