List questions from generalized-inverse

Published on 25 Oct 2016 - 19:25

44

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When $A=BC$ where $B$ is a singular, can we find an explicit form of $C$?

Published on 14 Feb 2017 - 0:09

69

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$(AB)^-=B^-A^{-1}$ holds when $A$ is nonsingular and $B$ is singular?

Published on 14 Feb 2017 - 18:56

42

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The equivalent definition of Moore-Penrose inverse based on projectors.

Published on 14 Jun 2023 - 13:13

25

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Explicit form of the left limit of the generalized inverse of a non-decreasing function

Published on 14 Jul 2023 - 13:22

57

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$A^{-}A$ and $AA^{-}$ are symmetric when $A^{-}$ is reflexive

Published on 01 Oct 2023 - 12:24

115

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For ($n \times p$) $A = \begin{bmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \\ \end{bmatrix} $, show that $A_{22} = A_{21}A_{11}^{-1}A_{12}$

Published on 19 Oct 2023 - 0:12

24

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Demonstrate the solutions of a linear system of equations with A matrix, while B being A's generalized inverse

Published on 23 Oct 2023 - 16:15

36

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Question related to splitting of matrix

Published on 27 Feb 2024 - 5:08

316

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One-sided inverses of a stochastic matrix

Published on 30 Sep 2015 - 14:48

201

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A question about generalized inverse matrix

Published on 29 Oct 2015 - 7:27

684

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Convergence of generalized inverses

Published on 07 Nov 2015 - 8:21

63

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How we can find the eigen values?

Published on 27 Nov 2015 - 10:49

112

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$r(X) = r(P_{X}) = \text{tr}(P_X)$

Published on 28 Dec 2015 - 21:12

104

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A has a group inverse if and only if its index is 1

Published on 02 Jun 2016 - 7:13

List Question

What do we call different full row rank matrices with the same inverse?

When $A=BC$ where $B$ is a singular, can we find an explicit form of $C$?

$(AB)^-=B^-A^{-1}$ holds when $A$ is nonsingular and $B$ is singular?

The equivalent definition of Moore-Penrose inverse based on projectors.

Explicit form of the left limit of the generalized inverse of a non-decreasing function

$A^{-}A$ and $AA^{-}$ are symmetric when $A^{-}$ is reflexive

For ($n \times p$) $A = \begin{bmatrix} A_{11} & A_{12} \\ A_{21} & A_{22} \\ \end{bmatrix} $, show that $A_{22} = A_{21}A_{11}^{-1}A_{12}$

Demonstrate the solutions of a linear system of equations with A matrix, while B being A's generalized inverse

Question related to splitting of matrix

One-sided inverses of a stochastic matrix

A question about generalized inverse matrix

Convergence of generalized inverses

How we can find the eigen values?

$r(X) = r(P_{X}) = \text{tr}(P_X)$

A has a group inverse if and only if its index is 1

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