Question

pseudoinverse under change of norm

score 47 · Answer 1 · 2013-03-07 18:35:54

47

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pseudoinverse under change of norm

Published on 07 Mar 2013 - 18:35

score 219 · Answer 2 · 2020-08-03 03:41:25

219

Views

Moore-Penrose Pseudoinverse: Because $(AA^+)^T = AA^+$, we have that $A^T(Ax-b) = ((AA^+)A)^Tb - A^Tb = 0$

Published on 03 Aug 2020 - 3:41

score 871 · Answer 3 · 2020-08-03 11:23:43

871

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Limit definition of pseudoinverse: $A^+ b$ is as close as possible to $y$ in terms of the Euclidean norm $\lVert Ax-b\rVert_2$

Published on 03 Aug 2020 - 11:23

score 70 · Answer 4 · 2020-08-03 14:23:51

70

Views

SVD definition of pseudoinverse: $A^+ b$ is as close as possible to $y$ in terms of the Euclidean norm $\lVert Ax-b\rVert_2$

Published on 03 Aug 2020 - 14:23

score 28 · Answer 5 · 2020-08-05 14:19:53

28

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Does $T (A T)^+ = A^+$ hold for invertible $T$ and full-row-rank $A$?

Published on 05 Aug 2020 - 14:19

score 5.1k · Answer 6 · 2020-08-05 16:56:55

5.1k

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Matrix multiplied by its pseudo-inverse doesn't give the identity matrix. Why?

Published on 05 Aug 2020 - 16:56

score 892 · Answer 7 · 2020-08-12 14:05:59

892

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Pseudoinverse of the pseudoinverse of a matrix

Published on 12 Aug 2020 - 14:05

score 152 · Answer 8 · 2020-08-13 07:45:27

152

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Moore-Penrose inverse of a block matrix

Published on 13 Aug 2020 - 7:45

score 1.5k · Answer 9 · 2020-08-18 05:05:12

1.5k

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Pseudoinverse of a diagonal matrix

Published on 18 Aug 2020 - 5:05

score 168 · Answer 10 · 2020-09-01 02:48:11

168

Views

Generalized Inverse of Block Matrix

Published on 01 Sep 2020 - 2:48

score 17 · Answer 11 · 2020-09-17 08:20:58

17

Views

Pseudoinverse of matrix product with multiple factors

Published on 17 Sep 2020 - 8:20

score 47 · Answer 12 · 2026-03-25 22:30:46

47

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$\left[\operatorname{cond}(A)\right]^2 = \|{A}\|^2\|\left(A^TA\right)^{-1}\|$ for $m \times n$ matrix $A, m > n.$

Published on 25 Mar 2026 - 22:30

score 84 · Answer 13 · 2026-03-25 07:42:14

84

Views

Do matrices with multiplication and Moore-Penrose inverse form a regular semigroupoid?

Published on 25 Mar 2026 - 7:42

score 40 · Answer 14 · 2020-09-23 21:50:38

40

Views

Generalized inverse of orthogonal perpendicular matrix

Published on 23 Sep 2020 - 21:50

score 199 · Answer 15 · 2020-09-23 22:47:45

199

Views

the pseudoinverse of a matrix with multiple rank one update

Published on 23 Sep 2020 - 22:47

List Question

pseudoinverse under change of norm

Moore-Penrose Pseudoinverse: Because $(AA^+)^T = AA^+$, we have that $A^T(Ax-b) = ((AA^+)A)^Tb - A^Tb = 0$

Limit definition of pseudoinverse: $A^+ b$ is as close as possible to $y$ in terms of the Euclidean norm $\lVert Ax-b\rVert_2$

SVD definition of pseudoinverse: $A^+ b$ is as close as possible to $y$ in terms of the Euclidean norm $\lVert Ax-b\rVert_2$

Does $T (A T)^+ = A^+$ hold for invertible $T$ and full-row-rank $A$?

Matrix multiplied by its pseudo-inverse doesn't give the identity matrix. Why?

Pseudoinverse of the pseudoinverse of a matrix

Moore-Penrose inverse of a block matrix

Pseudoinverse of a diagonal matrix

Generalized Inverse of Block Matrix

Pseudoinverse of matrix product with multiple factors

$\left[\operatorname{cond}(A)\right]^2 = \|{A}\|^2\|\left(A^TA\right)^{-1}\|$ for $m \times n$ matrix $A, m > n.$

Do matrices with multiplication and Moore-Penrose inverse form a regular semigroupoid?

Generalized inverse of orthogonal perpendicular matrix

the pseudoinverse of a matrix with multiple rank one update

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