Question

If v ∈ R^n is a nonzero vector, and I ∈ R^n×n is an identify matrix. Prove that M = I − 2(v(v^T)/||v||^2 is symmetric and satisfies M^−1 = M

score 126 · Answer 1 · 2018-10-19 20:16:24

126

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If v ∈ R^n is a nonzero vector, and I ∈ R^n×n is an identify matrix. Prove that M = I − 2(v(v^T)/||v||^2 is symmetric and satisfies M^−1 = M

Published on 19 Oct 2018 - 20:16

score 2.8k · Answer 2 · 2018-10-20 08:33:59

2.8k

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Find the minimum value of the quadratic form $x^TMx$ and the corresponding $x$, where $M$ is a symmetric matrix

Published on 20 Oct 2018 - 8:33

score 328 · Answer 3 · 2018-10-20 22:16:49

328

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Eigenvalue properties of matrix whose element-wise absolute value is row-stochastic

Published on 20 Oct 2018 - 22:16

score 88 · Answer 4 · 2026-03-22 16:30:32

88

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score 26 · Answer 5 · 2018-10-24 17:05:07

26

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score 227 · Answer 6 · 2026-03-25 07:43:56

227

Views

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score 105 · Answer 7 · 2026-03-25 03:01:07

105

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score 265 · Answer 8 · 2018-10-25 23:40:27

265

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score 430 · Answer 9 · 2026-03-26 06:21:38

430

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409

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score 123 · Answer 11 · 2018-10-29 08:45:54

123

Views

Is it true that $L+L^T$ has at most one negative eigenvalue?

Published on 29 Oct 2018 - 8:45

score 351 · Answer 12 · 2018-10-29 10:59:43

351

Views

strongly connected $L$, then what are the eigenvalues of $L+L^T$?

Published on 29 Oct 2018 - 10:59

score 71 · Answer 13 · 2018-11-09 06:51:29

71

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Published on 09 Nov 2018 - 6:51

score 1.4k · Answer 14 · 2026-03-12 02:34:56

1.4k

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Published on 12 Mar 2026 - 2:34

score 126 · Answer 15 · 2018-11-09 23:03:02

126

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List Question

If v ∈ R^n is a nonzero vector, and I ∈ R^n×n is an identify matrix. Prove that M = I − 2(v(v^T)/||v||^2 is symmetric and satisfies M^−1 = M

Find the minimum value of the quadratic form $x^TMx$ and the corresponding $x$, where $M$ is a symmetric matrix

Eigenvalue properties of matrix whose element-wise absolute value is row-stochastic

Numerically determine eigenvalues of real non-symmetric matrix known to have positive eigenvalues

Generalizing in matrix form

Relationships between top-$k$ eigenvector and top-$k$ singular vector of symmetric matrix $A$

can we perform SVD in spectral clustering to get top-$k$ eigenvector?

Eigenvectors with same eigenvalue

Proof of orthogonal and symmetric.

How many positive eigenvalues for a symmetric doubly stochastic matrix?

Is it true that $L+L^T$ has at most one negative eigenvalue?

strongly connected $L$, then what are the eigenvalues of $L+L^T$?

Find a real symmetric matrix $A$

Inverse of tridiagonal Toeplitz matrix

Trace inequality for a symmetric matrix

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