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 matrix-theory
Search options answers only
not deleted
user 297
Matrix theory is the study of matrices as concrete objects, rather than as abstract linear operators between vector spaces (whose study belongs to linear algebra). For instance, this involves matrix factorizations and decompositions, nonnegative matrices and Perron-Frobenius theory, Schur complements, structured and special matrices, matrix functions and equations.
8
votes
Is the determinant the only multiplicative matrix function?
With the exception of $GL_2(\mathbb{F}_2)$, the commutator subgroup of $GL_n(k)$ is $SL_n(k)$ (for $k$ a field). So any multiplicative map from $GL_n(k)$ to an abelian group factors through determinan …
- 156k
6
votes
The sum of squared logarithms conjecture
Lev Borisov having put up a complete solution; I'll put up how far I got. In his notation, I was able to show $\frac{\partial f(a)}{\partial a_k} > 0$ when $z^n + a_{n-1} z^{n-1} + \cdots + a_0$ has a …
- 156k
8
votes
Accepted
How wide is the Birkhoff Polytope?
For $n$ even, the width is exactly $\frac{2}{\sqrt{n-1}}$. For $n$ odd, I can prove this as a lower bound and $\frac{2n}{(n-1) \sqrt{n+1}} = \frac{2}{\sqrt{n-1} \sqrt{1-1/n^2}}$ as an upper bound.
…
- 156k
3
votes
Find a square, stochastic matrix of odd size, not a permutation matrix, with an eigenvalue o...
If you want a doubly stochastic matrix,
$$\begin{pmatrix}
0&1 & 0&0&0 \\
1&0 & 0&0&0 \\
0&0 & 1/3&1/3&1/3 \\
0&0 & 1/3&1/3&1/3 \\
0&0 & 1/3&1/3&1/3 \\
\end{pmatrix}$$
has eigenvalue $-1$.
- 156k
6
votes
Orthogonal basis of ${\bf Sym}_n(\mathbb R)$, made of orthogonal matrices
If there is a Hadamard matrix of size $n/2$, then there is a set of orthogonal matrices as desired. Recall that Hadamard's conjecture predicts that there is a Hadamard matrix of size $m$ whenever $m \ …
- 156k