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Results tagged with matrices
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user 43954
Questions where the notion matrix has an important or crucial role (for the latter, note the tag matrix-theory for potential use). Matrices appear in various parts of mathematics, and this tag is typically combined with other tags to make the general subject clear, such as an appropriate top-level tag ra.rings-and-algebras, co.combinatorics, etc. and other tags that might be applicable. There are also several more specialized tags concerning matrices.
1
vote
Accepted
Selecting columns of a set of boolean matrices with constraint on the ones in each row
For any natural number $k$ put $n=2^k$ and consider matrices $A_1,\dots, A_k$, where each $A_j$ consists of $n/2$ copies of columns $a_j^T=(a_{ij})$, where $a_{ij}=1$, if $\lfloor i/2^{j-1} \rfloor$ is …
- 5,409
4
votes
Accepted
How flexible is the infinite-dimensional torus?
This is a draft proof of an affirmative answer to Problem 3.
Proposition. For any $n\in\mathbb N$, $\varepsilon>0$ and vectors $x_1,\dots,x_n\in\mathbb R^{2n}$ there exists a linear transformation $ …
- 5,409
2
votes
Smith normal form and last invariant factor of certain matrices
We consider the following matrices over the field $\mathbb Z_p$ of residues modulo $p$. … If the last row of $Z$ is zero then both matrices $N_1$ and $N_2$ are singular and we ore done. …
- 5,409
2
votes
Visualizing the elements of a finite group and does the Gram matrix determine the finite group?
Let $\phi(\pi(1))$ and $\phi(\pi(h))$ be the $n\times m$ matrices $\|e_{ij}\|$ and $\|h_{ij}\|$, respectively. …
- 5,409