Question

How to prove $\mathbf{1}^\top\mathbf{Q}^+\mathbf{Q}=\mathbf{1}^\top$, where $\mathbf{Q}$ is any element-wise squared correlation matrix?

score 313 · Answer 1 · 2026-03-26 10:46:14

313

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How to prove $\mathbf{1}^\top\mathbf{Q}^+\mathbf{Q}=\mathbf{1}^\top$, where $\mathbf{Q}$ is any element-wise squared correlation matrix?

Published on 26 Mar 2026 - 10:46

score 117 · Answer 2 · 2023-07-27 19:39:16

117

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41

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40

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score 31 · Answer 5 · 2023-09-30 17:21:35

31

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28

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score 46 · Answer 7 · 2023-10-10 07:18:30

46

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score 45 · Answer 8 · 2023-10-16 06:24:19

45

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score 116 · Answer 9 · 2026-03-18 00:43:29

116

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score 87 · Answer 10 · 2023-10-19 15:53:01

87

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score 44 · Answer 11 · 2023-10-27 21:21:32

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103

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score 44 · Answer 14 · 2023-11-19 15:53:12

44

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score 42 · Answer 15 · 2023-11-26 14:16:30

42

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List Question

How to prove $\mathbf{1}^\top\mathbf{Q}^+\mathbf{Q}=\mathbf{1}^\top$, where $\mathbf{Q}$ is any element-wise squared correlation matrix?

Solve a linear equation XA=B using matrix with zero diagonal

L2 Norm of Pseudo-Inverse Relation with Minimum Singular Value formal source?

Expectation of the pseudoinverse of a complex Gaussian matrix with non identically distributed columns

Solving for a dot product operand

Use of the inequality $A \succeq B^{\dagger}$ when B is not invertible

Simplifying a matrix expression that involves a Moore-Penrose pseudoinverse

For $m \times n$ matrix $A$ with $m \ge n$, show ${\lVert A^+ \rVert}_2 = 1/\sigma_n$ where $A^+ = (A^A)^{-1} A^$

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

Procedure to generate an inverse for a non-square matrix

Moore-Penrose inverse error approximation for matrix product

Transform multiplicative noise to additive noise with singular matrices

Pseudo-inverse matrix to minimise $L^1$ norm error

One quick question about Moore–Penrose inverse of a symmetric matrix

Validation of Normal Equations with Pseudo-Inverses

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