List questions from matrix-exponential

Published on 15 Apr 2026 - 20:31

109

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For real square matrices $A_0,A_1$ with $(A^{T}_0+A_0)+(A^{T}_{1}+A_1)\leq{-\gamma{I}}$, is it possible to prove the following inequality?

Published on 15 Apr 2026 - 3:21

109

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Let $A$ be a complex matrix $n \times n$ matrix. Suppose that $e^{A} = I + A + A^{2}$. Prove or disprove: A is the zero matrix.

Published on 13 Apr 2026 - 23:33

223

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Exists an exponential matrix

Published on 14 Apr 2026 - 4:31

76

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For a real square matrix $A$ with all eigenvalues on the imaginary axis, does the following hold?

Published on 16 Apr 2026 - 18:06

334

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convergence of matrix exponential as matrix converges entrywisely

Published on 14 Apr 2026 - 1:47

620

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If the exponential of matrices equals the identity. Could they fail to commute?

Published on 12 Apr 2026 - 8:34

251

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find exponential of 4x4 matrix

Published on 13 Apr 2026 - 21:29

80

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Eigenvalues and eigenvectors of $4\times 4$ matrix

Published on 09 Apr 2026 - 4:39

670

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Explicit formula of exponential of companion matrix

Published on 23 Apr 2026 - 19:15

552

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3x3 integer matrix

Published on 13 Apr 2026 - 16:37

50

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matrix exponential - Is such behavior expected?

Published on 14 Apr 2026 - 9:52

135

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Matrix exponentials, computing the product of $\exp(-iBt)$ and $\exp(-iB^{-1}t)$.

Published on 15 Apr 2026 - 23:03

383

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On the commutativity of matrices and their exponentials

Published on 14 Apr 2026 - 6:14

97

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Is there any complex number $a$ solving $\exp (X)=1+aX$ for given square matrix $X$?

Published on 15 Apr 2026 - 2:43

List Question

For real square matrices of the same dimension, does the following hold?

For real square matrices $A_0,A_1$ with $(A^{T}_0+A_0)+(A^{T}_{1}+A_1)\leq{-\gamma{I}}$, is it possible to prove the following inequality?

Let $A$ be a complex matrix $n \times n$ matrix. Suppose that $e^{A} = I + A + A^{2}$. Prove or disprove: A is the zero matrix.

Exists an exponential matrix

For a real square matrix $A$ with all eigenvalues on the imaginary axis, does the following hold?

convergence of matrix exponential as matrix converges entrywisely

If the exponential of matrices equals the identity. Could they fail to commute?

find exponential of 4x4 matrix

Eigenvalues and eigenvectors of $4\times 4$ matrix

Explicit formula of exponential of companion matrix

3x3 integer matrix

matrix exponential - Is such behavior expected?

Matrix exponentials, computing the product of $\exp(-iBt)$ and $\exp(-iB^{-1}t)$.

On the commutativity of matrices and their exponentials

Is there any complex number $a$ solving $\exp (X)=1+aX$ for given square matrix $X$?

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