Search Results
| Search type | Search syntax |
|---|---|
| Tags | [tag] |
| Exact | "words here" |
| Author |
user:1234 user:me (yours) |
| Score |
score:3 (3+) score:0 (none) |
| Answers |
answers:3 (3+) answers:0 (none) isaccepted:yes hasaccepted:no inquestion:1234 |
| Views | views:250 |
| Code | code:"if (foo != bar)" |
| Sections |
title:apples body:"apples oranges" |
| URL | url:"*.example.com" |
| Saves | in:saves |
| Status |
closed:yes duplicate:no migrated:no wiki:no |
| Types |
is:question is:answer |
| Exclude |
-[tag] -apples |
| For more details on advanced search visit our help page | |
Results tagged with linear-algebra
Search options not deleted
user 2757
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
14
votes
Accepted
Waring's problem for matrices
The answer is YES if $n$ is even. But if $n$ is odd, then the answer is NO since $-I$ is not a sum of two squares.
See
Griffin and Krusemeyer, Matrices as sums of squares, Linear and Multilinear Al …
- 23.8k
16
votes
Accepted
Spheres over rational numbers and other fields
Any orthonormal set extends to an orthonormal basis, over any field
of characteristic not $2$. This is a special case of Witt's theorem.
EDIT: In response to Vipul's comment: The proof of Witt's the …
- 23.8k
46
votes
1
answer
6k
views
Determinant of a determinant
Consider an $mn \times mn$ matrix over a commutative ring $A$, divided into $n \times n$ blocks that commute pairwise. One can pretend that each of the $m^2$ blocks is a number and apply the $m \time …
- 23.8k
11
votes
Accepted
Surjectivity of bilinear forms.
The answer to Question B is no, as I'll show below.
Let $U=V=\mathbf{Q}^3$ and $W=\mathbf{Q}^4$. Define
$$\beta((u_1,u_2,u_3),(v_1,v_2,v_3))=(u_1 v_1,u_2 v_2,u_3 v_3, (u_1+u_2+u_3)(v_1+v_2+v_3)).$$
…
- 23.8k