List questions from matrix-exponential

Published on 16 Mar 2021 - 18:02

96

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Suppose we have a matrix $A(t) = \exp(tB)$ whose entries are all positive for some $t$, how can I show that $\exp(tB)$ is positive for all $t$?

Published on 31 Mar 2021 - 22:39

109

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How to prove that $\exp\left(\mathbf{A}\right)=-\mathbf{I}$ for given $\mathbf{A}$?

Published on 04 Apr 2021 - 21:27

130

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Can you generate all unitary operators from the unit ball of Hermitian operators?

Published on 26 Mar 2026 - 19:18

188

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Understanding: Differental of Riemannian exponential expressed through Jacobi-Fields

Published on 26 Mar 2026 - 9:41

116

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Find matrix exponential of a Jordan matrix

Published on 08 Apr 2021 - 4:07

41

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Can you define sine and cosine in the complex numbers?

Published on 11 Apr 2021 - 20:30

287

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Prove $e^{T^{-1}AT} = T^{-1}e^AT$.

Published on 19 Apr 2021 - 11:17

475

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Find $e^{At}$ of the matrix given below.

Published on 22 Apr 2021 - 21:16

81

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2 to the power of a matrix

Published on 23 Apr 2021 - 10:35

58

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Proof that matrix exponent elements belong to certain span

Published on 03 May 2021 - 12:01

58

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Integrate $\int_0^t e^{sA}e^{sA^T}ds$ when $A$ is invertible but not normal

Published on 10 May 2021 - 6:39

96

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How to prove $\lim_{h\rightarrow 0} \frac{\exp\left\{\int_t ^{t+h}A(s)\,\mathrm{d}s\right\}-I_n}{h}=A(t)$

Published on 14 May 2021 - 23:04

69

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Distance of matrices

Published on 15 May 2021 - 13:44

248

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Infinitesimal generator of continuous time Markov chain (exponential of a matrix)

Published on 16 May 2021 - 14:42

List Question

Use of the right Jacobian in SO(3) to approximate $\exp([\phi + \delta\phi]_\times)$

Suppose we have a matrix $A(t) = \exp(tB)$ whose entries are all positive for some $t$, how can I show that $\exp(tB)$ is positive for all $t$?

How to prove that $\exp\left(\mathbf{A}\right)=-\mathbf{I}$ for given $\mathbf{A}$?

Can you generate all unitary operators from the unit ball of Hermitian operators?

Understanding: Differental of Riemannian exponential expressed through Jacobi-Fields

Find matrix exponential of a Jordan matrix

Can you define sine and cosine in the complex numbers?

Prove $e^{T^{-1}AT} = T^{-1}e^AT$.

Find $e^{At}$ of the matrix given below.

2 to the power of a matrix

Proof that matrix exponent elements belong to certain span

Integrate $\int_0^t e^{sA}e^{sA^T}ds$ when $A$ is invertible but not normal

How to prove $\lim_{h\rightarrow 0} \frac{\exp\left\{\int_t ^{t+h}A(s)\,\mathrm{d}s\right\}-I_n}{h}=A(t)$

Distance of matrices

Infinitesimal generator of continuous time Markov chain (exponential of a matrix)

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