Question

Why is the sum of outer products equal to the matrix product of a matrix and its transpose , so $A^TA = \sum_{i=1}^n a_i a_i^T$?

score 2.7k · Answer 1 · 2026-04-17 00:28:01

2.7k

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Why is the sum of outer products equal to the matrix product of a matrix and its transpose , so $A^TA = \sum_{i=1}^n a_i a_i^T$?

Published on 17 Apr 2026 - 0:28

score 40 · Answer 2 · 2026-04-14 21:44:27

40

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Combination of an entry of a matrix in multiplicative form

Published on 14 Apr 2026 - 21:44

score 102 · Answer 3 · 2026-04-11 08:25:12

102

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Image of linear transformation of subspaces

Published on 11 Apr 2026 - 8:25

score 361 · Answer 4 · 2026-04-14 23:08:23

361

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If I have $A(AA)^{-1} A$ where $A$ is an $n \times n$ matrix, will I get the Identity matrix?

Published on 14 Apr 2026 - 23:08

score 30 · Answer 5 · 2026-04-11 00:00:09

30

Views

IFF statement reworded, which is equivalent?

Published on 11 Apr 2026 - 0:00

score 48 · Answer 6 · 2026-04-13 00:50:54

48

Views

Let $\|.\|$ be a norm on $\mathbb{R}^n$, and let $A$ be an $n\times n$ matrix. Put $\|x\|'=\|Ax\|$. What are the precise conditions on $A$ to ensure

Published on 13 Apr 2026 - 0:50

score 6.8k · Answer 7 · 2026-04-20 07:11:14

6.8k

Views

Frobenius and operator norms of rank 1 matrices

Published on 20 Apr 2026 - 7:11

score 42 · Answer 8 · 2026-03-25 06:08:28

42

Views

Two equivalent ways of polynomial regression?

Published on 25 Mar 2026 - 6:08

score 47 · Answer 9 · 2026-04-16 13:46:32

47

Views

N x N matrix has N nonzero eigenvalues but has the zero-vector as eigenvector

Published on 16 Apr 2026 - 13:46

score 72 · Answer 10 · 2026-04-09 11:06:50

72

Views

Complex Numbers expression

Published on 09 Apr 2026 - 11:06

score 1.3k · Answer 11 · 2026-04-16 21:00:54

1.3k

Views

Show that every subspace of R2 is one of the following: the trivial subspace {0}, a line through the origin, or R2 itself

Published on 16 Apr 2026 - 21:00

score 398 · Answer 12 · 2026-03-27 00:05:58

398

Views

Prove that if $A$ is diagonally dominant and if $Q$ is chosen as in the Jacobi method, then $\rho(I-Q^{-1}A)<1$

Published on 27 Mar 2026 - 0:05

score 237 · Answer 13 · 2026-04-11 08:55:02

237

Views

Matrix Representation Theorem with Differentiation Question

Published on 11 Apr 2026 - 8:55

score 51 · Answer 14 · 2026-04-08 00:17:49

51

Views

Is it possible determine reduction costs from the vector of duals?

Published on 08 Apr 2026 - 0:17

score 314 · Answer 15 · 2026-04-13 14:17:55

314

Views

How to combine 2 3x3 matrices into a single matrice to find span and check whether is it linearly independent

Published on 13 Apr 2026 - 14:17

List Question

Why is the sum of outer products equal to the matrix product of a matrix and its transpose , so $A^TA = \sum_{i=1}^n a_i a_i^T$?

Combination of an entry of a matrix in multiplicative form

Image of linear transformation of subspaces

If I have $A(AA)^{-1} A$ where $A$ is an $n \times n$ matrix, will I get the Identity matrix?

IFF statement reworded, which is equivalent?

Let $\|.\|$ be a norm on $\mathbb{R}^n$, and let $A$ be an $n\times n$ matrix. Put $\|x\|'=\|Ax\|$. What are the precise conditions on $A$ to ensure

Frobenius and operator norms of rank 1 matrices

Two equivalent ways of polynomial regression?

N x N matrix has N nonzero eigenvalues but has the zero-vector as eigenvector

Complex Numbers expression

Show that every subspace of R2 is one of the following: the trivial subspace {0}, a line through the origin, or R2 itself

Prove that if $A$ is diagonally dominant and if $Q$ is chosen as in the Jacobi method, then $\rho(I-Q^{-1}A)<1$

Matrix Representation Theorem with Differentiation Question

Is it possible determine reduction costs from the vector of duals?

How to combine 2 3x3 matrices into a single matrice to find span and check whether is it linearly independent

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