Question

In the SVD of $A = U \Sigma V^T$, how does one know that V actually spans the row space $C(A^T)$ of A and U the column space $C(A)$?

score 855 · Answer 1 · 2026-03-29 13:40:47

855

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In the SVD of $A = U \Sigma V^T$, how does one know that V actually spans the row space $C(A^T)$ of A and U the column space $C(A)$?

Published on 29 Mar 2026 - 13:40

score 1k · Answer 2 · 2015-01-22 09:03:32

1k

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If two matrices have the same characteristic polynomials, determinant and trace, are they similar?

Published on 22 Jan 2015 - 9:03

score 1k · Answer 3 · 2026-03-28 14:07:43

1k

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Is LU decomposition of matrices efficient for today's standards?

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score 2.3k · Answer 4 · 2026-03-28 02:06:39

2.3k

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score 1.2k · Answer 5 · 2026-03-25 03:24:22

1.2k

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score 187 · Answer 6 · 2015-01-30 14:29:52

187

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Published on 30 Jan 2015 - 14:29

score 241 · Answer 7 · 2015-01-30 18:44:57

241

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score 869 · Answer 8 · 2015-01-31 15:21:34

869

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116

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score 350 · Answer 10 · 2015-02-02 17:28:24

350

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score 47 · Answer 11 · 2015-02-03 21:03:50

47

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Published on 03 Feb 2015 - 21:03

score 55 · Answer 12 · 2015-02-04 06:33:23

55

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score 153 · Answer 13 · 2015-02-05 09:58:07

153

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Published on 05 Feb 2015 - 9:58

score 3k · Answer 14 · 2026-03-31 03:39:02

3k

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If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$

Published on 31 Mar 2026 - 3:39

score 196 · Answer 15 · 2015-02-09 13:52:18

196

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Question on congruence of diagonal matrices over $\mathbb R$

Published on 09 Feb 2015 - 13:52

List Question

In the SVD of $A = U \Sigma V^T$, how does one know that V actually spans the row space $C(A^T)$ of A and U the column space $C(A)$?

If two matrices have the same characteristic polynomials, determinant and trace, are they similar?

Is LU decomposition of matrices efficient for today's standards?

Decomposition of 4x4 or larger affine transformation matrix to individual variables per degree of freedom

Triangularization of a matrix

Is there a formula for the sum of absolute eigenvalues in terms of matrix elements?

Inversing badly-conditioned square matrix: methodology

unitary matrix decomposition using orthogonal matrices

Proving Frobenius Theorem for Eigen Values

Is this some kind of Perron-Frobenius theorem?

Invertible product of different-dimensional matrices

Orthogonal decomposition of a Matrix with constraints

LU Decomposition

If $\mathrm{Tr}(A)=0$ then $T=R^{-1}AR$ has all entries on its main diagonal equal to $0$

Question on congruence of diagonal matrices over $\mathbb R$

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