Question

Let A be an $n \times k$ matrix with $W$ as the column space. Show that the solution space of $A(A^T) x = 0$ is given by $W^⊥$.

score 172 · Answer 1 · 2026-03-31 03:39:08

172

Views

Let A be an $n \times k$ matrix with $W$ as the column space. Show that the solution space of $A(A^T) x = 0$ is given by $W^⊥$.

Published on 31 Mar 2026 - 3:39

score 224 · Answer 2 · 2021-10-23 03:38:43

224

Views

If $B$ is full rank, is $\text{rank}(AB)$ = $\text{rank}(A)$?

Published on 23 Oct 2021 - 3:38

score 220 · Answer 3 · 2021-10-23 15:12:00

220

Views

rank $k$ implies nonzero minor of size $k \times k$ but for for the vacuous case of $k=0$

Published on 23 Oct 2021 - 15:12

score 167 · Answer 4 · 2021-10-23 15:31:44

167

Views

If minor refers to determinant, then what do you call the matrix? Can I just say 'minor determinant' vs 'minor matrix'?

Published on 23 Oct 2021 - 15:31

score 408 · Answer 5 · 2021-10-23 18:33:42

408

Views

rank $n-1$ implies nonzero minor of size $(n-1) \times (n-1)$

Published on 23 Oct 2021 - 18:33

score 43 · Answer 6 · 2026-02-23 04:57:27

43

Views

Calculate maximum number of independent columns of a modular matrix

Published on 23 Feb 2026 - 4:57

score 996 · Answer 7 · 2026-03-28 20:54:03

996

Views

Prove that projection matrix has the same rank as design matrix.

Published on 28 Mar 2026 - 20:54

score 31 · Answer 8 · 2021-10-31 10:05:42

31

Views

Weighted low-rank approximation with convex constraint

Published on 31 Oct 2021 - 10:05

score 74 · Answer 9 · 2021-10-31 16:48:10

74

Views

Rank and Nullity of Transformation

Published on 31 Oct 2021 - 16:48

score 183 · Answer 10 · 2026-03-29 20:39:34

183

Views

Does $ \mbox{rank} (A B) \leq \min \left( \mbox{rank} (A), \mbox{rank}(B) \right)$ hold with probability $1$ when matrices $A$ and $B$ are random?

Published on 29 Mar 2026 - 20:39

score 115 · Answer 11 · 2021-11-02 19:03:36

115

Views

Finding the rank of a matrix from its eigenvalues without using the rank-nullity theorem.

Published on 02 Nov 2021 - 19:03

score 82 · Answer 12 · 2021-11-03 02:30:17

82

Views

Nystrom method matrix approximation error dependency on the spectrum of the matrix to be approximated

Published on 03 Nov 2021 - 2:30

score 47 · Answer 13 · 2021-11-04 02:48:26

47

Views

Vectors with 5-coordinates seemingly 3 Dimensional

Published on 04 Nov 2021 - 2:48

score 204 · Answer 14 · 2021-11-05 01:41:15

204

Views

The rank of a matrix. Inequality and eqality proofs

Published on 05 Nov 2021 - 1:41

score 190 · Answer 15 · 2026-04-01 06:29:51

190

Views

When does an frame of rank $n$ contain $n$ orthonormal vectors?

Published on 01 Apr 2026 - 6:29

List Question

Let A be an $n \times k$ matrix with $W$ as the column space. Show that the solution space of $A(A^T) x = 0$ is given by $W^⊥$.

If $B$ is full rank, is $\text{rank}(AB)$ = $\text{rank}(A)$?

rank $k$ implies nonzero minor of size $k \times k$ but for for the vacuous case of $k=0$

If minor refers to determinant, then what do you call the matrix? Can I just say 'minor determinant' vs 'minor matrix'?

rank $n-1$ implies nonzero minor of size $(n-1) \times (n-1)$

Calculate maximum number of independent columns of a modular matrix

Prove that projection matrix has the same rank as design matrix.

Weighted low-rank approximation with convex constraint

Rank and Nullity of Transformation

Does $ \mbox{rank} (A B) \leq \min \left( \mbox{rank} (A), \mbox{rank}(B) \right)$ hold with probability $1$ when matrices $A$ and $B$ are random?

Finding the rank of a matrix from its eigenvalues without using the rank-nullity theorem.

Nystrom method matrix approximation error dependency on the spectrum of the matrix to be approximated

Vectors with 5-coordinates seemingly 3 Dimensional

The rank of a matrix. Inequality and eqality proofs

When does an frame of rank $n$ contain $n$ orthonormal vectors?

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