Question

alVerify that $X^TX=\sum^3_{i=1}X_iX^T_i$ letting $X=\begin{bmatrix} 1&2 \\ 2&5 \\ 0&3\end{bmatrix}$ and $X^T_i$ be the ith row of X.

score 37 · Answer 1 · 2016-03-24 01:19:49

37

Views

alVerify that $X^TX=\sum^3_{i=1}X_iX^T_i$ letting $X=\begin{bmatrix} 1&2 \\ 2&5 \\ 0&3\end{bmatrix}$ and $X^T_i$ be the ith row of X.

Published on 24 Mar 2016 - 1:19

score 2.3k · Answer 2 · 2026-04-12 04:35:40

2.3k

Views

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Published on 12 Apr 2026 - 4:35

score 68 · Answer 3 · 2026-04-13 10:44:19

68

Views

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score 141 · Answer 4 · 2016-03-24 23:48:51

141

Views

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Published on 24 Mar 2016 - 23:48

score 163 · Answer 5 · 2026-04-13 06:43:32

163

Views

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score 399 · Answer 6 · 2016-03-26 12:26:10

399

Views

For invertible $A$, $C$, prove that: $(A^{−1} + B^TC^{−1}B)^{−1}B^TC^{−1} = AB^T(BAB^T + C)^{−1}$

Published on 26 Mar 2016 - 12:26

score 494 · Answer 7 · 2026-04-11 05:16:22

494

Views

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score 44 · Answer 8 · 2026-04-13 07:13:04

44

Views

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14.1k

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score 1k · Answer 10 · 2026-04-11 08:12:13

1k

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score 16.9k · Answer 11 · 2026-04-12 04:34:45

16.9k

Views

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Published on 12 Apr 2026 - 4:34

score 259 · Answer 12 · 2016-04-01 13:27:53

259

Views

$A,B \in M_n(\mathbb{R})$ are similar over $\mathbb{R}$ if they are similar over $\mathbb{C}$

Published on 01 Apr 2016 - 13:27

score 490 · Answer 13 · 2016-04-03 04:02:42

490

Views

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Published on 03 Apr 2016 - 4:02

score 26 · Answer 14 · 2016-04-03 19:51:55

26

Views

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Published on 03 Apr 2016 - 19:51

score 173 · Answer 15 · 2026-04-11 15:01:16

173

Views

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List Question

alVerify that $X^TX=\sum^3_{i=1}X_iX^T_i$ letting $X=\begin{bmatrix} 1&2 \\ 2&5 \\ 0&3\end{bmatrix}$ and $X^T_i$ be the ith row of X.

Properties of a square matrix whose rows and columns sum to form vectors orthogonal to the "all ones" vector?

Is there any way to make matrix multiplication 'act' commutative?

For invertible matrices $A$ and $C$, prove or disprove that $(C^{-1}BAB^T + I)$ is invertible.

Rotation of a matrix

For invertible $A$, $C$, prove that: $(A^{−1} + B^TC^{−1}B)^{−1}B^TC^{−1} = AB^T(BAB^T + C)^{−1}$

Rearranging a Matrix equation

Is my proof correct? (prequel to inverse matrices)

LU Decomposition vs. QR Decomposition for similar problems

How to express the 'general solution' of a matrix with a unique solution

In $Ax=b$. If $A$ is not invertible there are no solutions or infinity. How to determine what the case is?

$A,B \in M_n(\mathbb{R})$ are similar over $\mathbb{R}$ if they are similar over $\mathbb{C}$

All solutions of $A^2+I=0$ in $M(n,\mathbb{C})$ are similar

Values for $*$ symbol in linear algebra equation

Matrices and cofactors question

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