List questions from determinant

Published on 27 Jan 2018 - 23:28

169

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Let $A\in \mathbb{R}^{n\times n}$ be invertible such that $A$ and $A^{-1}$ have integer entries. Prove that $\det(A)\in\{-1,1\}$.

Published on 28 Jan 2018 - 2:30

47

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Find the general solution of linear system

Published on 25 Mar 2026 - 11:10

44

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Bounding the determinant of principal sub-matrices of the Kroneker product

Published on 23 Mar 2026 - 8:12

97

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Sum of subspaces by setting determinant = 0

Published on 22 Mar 2026 - 14:15

311

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Summation of determinants

Published on 21 Mar 2026 - 21:56

535

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Finding the eigenvalues of the transpose map.

Published on 24 Mar 2026 - 20:46

174

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Finding a matrix with conditions on $A^{-1}$ and $\det(A)=0.5$

Published on 30 Jan 2018 - 12:01

621

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Solve $n$th order determinant

Published on 22 Mar 2026 - 5:21

2.6k

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Why does computation of the determinant have anything to do with the "volume" of the fundamental "parallelepiped"?

Published on 24 Mar 2026 - 19:01

71

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Any trick to swap order of determinant and matrix inverse operation?

Published on 01 Feb 2018 - 6:05

1k

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Describe $\det(A^*)$ in terms of $\det(A)$

Published on 22 Mar 2026 - 9:05

37

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Integration of a determinant

Published on 21 Mar 2026 - 23:33

61

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Sufficient/necessary condition for submatrix determinant (minor) that decreases with size?

Published on 24 Mar 2026 - 21:08

117

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Determinant Problem

Published on 21 Mar 2026 - 18:01

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Let $A\in \mathcal {M}_n(\mathbb{F}_2)$ such that $A^3=I$. Find $\det(A)$

Let $A\in \mathbb{R}^{n\times n}$ be invertible such that $A$ and $A^{-1}$ have integer entries. Prove that $\det(A)\in\{-1,1\}$.

Find the general solution of linear system

Bounding the determinant of principal sub-matrices of the Kroneker product

Sum of subspaces by setting determinant = 0

Summation of determinants

Finding the eigenvalues of the transpose map.

Finding a matrix with conditions on $A^{-1}$ and $\det(A)=0.5$

Solve $n$th order determinant

Why does computation of the determinant have anything to do with the "volume" of the fundamental "parallelepiped"?

Any trick to swap order of determinant and matrix inverse operation?

Describe $\det(A^*)$ in terms of $\det(A)$

Integration of a determinant

Sufficient/necessary condition for submatrix determinant (minor) that decreases with size?

Determinant Problem

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