List questions from cayley-hamilton

Published on 29 Dec 2021 - 21:03

169

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Inverse of the Cayley-Hamilton theorem

Published on 19 Feb 2022 - 13:05

51

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Eigenvalue of a $3\times 3$ complex matrix

Published on 20 Feb 2022 - 8:40

99

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Finding $\det(f(A))$, given the eigenvalues of $A$.

Published on 19 Mar 2022 - 12:53

102

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How to express det (a(A-B) - bI)

Published on 23 Mar 2022 - 8:21

161

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Cayley-Hamilton Theorem explanation. I'm having trouble interpreting the meaning of $f(T)$.

Published on 06 Apr 2022 - 23:16

146

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Suppose that $f: V \to V$ is a $k$-linear transformation such that $f^m = 0$ for some integer $m.$ Prove that $f^n = 0.$

Published on 29 Apr 2022 - 11:27

56

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Understanding properties of a matrix $A\in \mathcal{M}_n({K})$ for which $C(A)=\{f(A): f(x) \in K[x]\}$.

Published on 03 Jul 2022 - 7:17

159

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Vandermonde matrix whose elements are different roots of unity

Published on 12 Jul 2022 - 1:37

216

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Algebraic Elements are Integral, if their Minimal Polynomial is.

Published on 13 Jul 2022 - 14:14

77

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Finding all polynomials $q,f$ such that $q(C)$ has non-zero kernel and $f(C)$ is invertible

Published on 21 Jul 2022 - 18:12

137

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Representation of fields with matrices

Published on 27 Jul 2022 - 21:54

70

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Is there any intuitive explanation to $A^2=\operatorname{tr}(A)A-\det(A)I_{2\times 2}$ for $A \in \mathbb{R}^{2\times 2}$?

Published on 17 Sep 2022 - 14:47

100

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Step in proof of Cayley-Hamilton theorem in Steinberg's book

Published on 11 Oct 2022 - 14:25

109

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If Cayley-Hamilton holds over $\mathbb{C}$ it holds over all unitary, commutative rings.

Published on 08 Nov 2022 - 5:17

List Question

Matrix exponential via Cayley-Hamilton

Inverse of the Cayley-Hamilton theorem

Eigenvalue of a $3\times 3$ complex matrix

Finding $\det(f(A))$, given the eigenvalues of $A$.

How to express det (a(A-B) - bI)

Cayley-Hamilton Theorem explanation. I'm having trouble interpreting the meaning of $f(T)$.

Suppose that $f: V \to V$ is a $k$-linear transformation such that $f^m = 0$ for some integer $m.$ Prove that $f^n = 0.$

Understanding properties of a matrix $A\in \mathcal{M}_n({K})$ for which $C(A)=\{f(A): f(x) \in K[x]\}$.

Vandermonde matrix whose elements are different roots of unity

Algebraic Elements are Integral, if their Minimal Polynomial is.

Finding all polynomials $q,f$ such that $q(C)$ has non-zero kernel and $f(C)$ is invertible

Representation of fields with matrices

Is there any intuitive explanation to $A^2=\operatorname{tr}(A)A-\det(A)I_{2\times 2}$ for $A \in \mathbb{R}^{2\times 2}$?

Step in proof of Cayley-Hamilton theorem in Steinberg's book

If Cayley-Hamilton holds over $\mathbb{C}$ it holds over all unitary, commutative rings.

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