Question

Dimensions of symmetric and skew-symmetric matrices

score 116.4k · Answer 1 · 2026-03-16 20:16:12

116.4k

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Dimensions of symmetric and skew-symmetric matrices

Published on 16 Mar 2026 - 20:16

score 3.8k · Answer 2 · 2026-03-17 04:29:05

3.8k

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If $A$ is skew-symmetric, then $I-A$ is invertible and $Q = (I-A)^{-1}(I+A)$ is orthogonal

Published on 17 Mar 2026 - 4:29

score 160 · Answer 3 · 2026-03-16 18:38:37

160

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If $A$ is skew-symmetric, then $x^T A^2 x \le 0$

Published on 16 Mar 2026 - 18:38

score 161 · Answer 4 · 2020-08-04 01:45:47

161

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Skew symmetric matrix of vector triple product

Published on 04 Aug 2020 - 1:45

score 132 · Answer 5 · 2020-08-07 19:15:45

132

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How can I prove $[r][\omega]^{2}r = -[\omega][r]^2\omega$?

Published on 07 Aug 2020 - 19:15

score 116 · Answer 6 · 2020-08-10 12:57:13

116

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Subring generated by the set of all symmetric matrices contains skew-symmetric matrices

Published on 10 Aug 2020 - 12:57

score 110 · Answer 7 · 2026-03-25 14:24:38

110

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Show that the group operation of conjugation is compatible with the bilinear form $\langle A,B\rangle=1/2 \textrm{ trace }AB$

Published on 25 Mar 2026 - 14:24

score 524 · Answer 8 · 2020-08-11 04:45:35

524

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Let $A, B$ be skew-symmetric matrices such that $AB = -BA$. Show that $AB = 0$

Published on 11 Aug 2020 - 4:45

score 242 · Answer 9 · 2020-08-26 11:28:59

242

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Eigenvalues of a skew-symmetric operator

Published on 26 Aug 2020 - 11:28

score 76 · Answer 10 · 2026-02-23 21:15:15

76

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Simultaneously writing several skew-symmetric matrices on a "canonical" form

Published on 23 Feb 2026 - 21:15

score 45 · Answer 11 · 2020-09-09 23:55:59

45

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Prove that $\int_0^1 {\bf v \, . \, W}(s)\: {\bf v} \, ds = 0$ for skew matrix $\bf W$ and vector $\bf v$

Published on 09 Sep 2020 - 23:55

score 149 · Answer 12 · 2020-09-18 12:02:39

149

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Is there a 'geometric' version of this derivation of the vorticity equation?

Published on 18 Sep 2020 - 12:02

score 56 · Answer 13 · 2020-10-01 06:15:06

56

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If $A$ is a real $n\times n$ matrix such that $AB=BA$ for any real skew-symmetric $n\times n$ matrix $B$, then $A=kI_n$ for some $k\in\mathbb{R}$.

Published on 01 Oct 2020 - 6:15

score 126 · Answer 14 · 2020-10-06 14:21:02

126

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Exponential map from o(n) to O(n)

Published on 06 Oct 2020 - 14:21

score 37 · Answer 15 · 2020-10-13 05:51:30

37

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Unclear statement on symmetric/skew symmetric matrices

Published on 13 Oct 2020 - 5:51

List Question

Dimensions of symmetric and skew-symmetric matrices

If $A$ is skew-symmetric, then $I-A$ is invertible and $Q = (I-A)^{-1}(I+A)$ is orthogonal

If $A$ is skew-symmetric, then $x^T A^2 x \le 0$

Skew symmetric matrix of vector triple product

How can I prove $[r][\omega]^{2}r = -[\omega][r]^2\omega$?

Subring generated by the set of all symmetric matrices contains skew-symmetric matrices

Show that the group operation of conjugation is compatible with the bilinear form $\langle A,B\rangle=1/2 \textrm{ trace }AB$

Let $A, B$ be skew-symmetric matrices such that $AB = -BA$. Show that $AB = 0$

Eigenvalues of a skew-symmetric operator

Simultaneously writing several skew-symmetric matrices on a "canonical" form

Prove that $\int_0^1 {\bf v \, . \, W}(s)\: {\bf v} \, ds = 0$ for skew matrix $\bf W$ and vector $\bf v$

Is there a 'geometric' version of this derivation of the vorticity equation?

If $A$ is a real $n\times n$ matrix such that $AB=BA$ for any real skew-symmetric $n\times n$ matrix $B$, then $A=kI_n$ for some $k\in\mathbb{R}$.

Exponential map from o(n) to O(n)

Unclear statement on symmetric/skew symmetric matrices

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