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Results tagged with matrices
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user 46140
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.
9
votes
Accepted
Efficiently computing $\prod_{i=1}^{n} A_i$
A_{u+2} \cdots A_{u+s}$ symbolically as a matrix of polynomials in $u$; use multi-point evaluation on each of the four polynomials for $u \in \{0,s,2s,\ldots,(s-1)s\}$; and multiply the $s$ resulting matrices …
- 7,226
5
votes
Accepted
Guess the next polynoms in the sequence (MO vs. AI :), count anticommuting $F_p$-matrices, P...
It's not entirely clear to me how much data your guesses are based on, so I present a table with calculated data and guessed polynomials based on that data and the assumption that $f(1) = f(-1) = 1$.
…
- 7,226
2
votes
Non-singular matrix with restricted entries
This answer gives constructions for singular matrices with the following factors:
$((k-1)x - ky + 1)$, so that there is a singular matrix if $x = y = 1 \pmod {x - y}$. … Certainly larger symmetric circulant block matrices don't help. Maybe this idea can't be pushed any further (although the theorem is certainly not nothing). …
- 7,226
2
votes
Accepted
Combinatorial graph optimization problem on integer adjacency matrices
Consider $$M_{i,j} = \begin{cases} 1 & \textrm{if } i \equiv j \pmod 2 \\ N & \textrm{if } i \not\equiv j \pmod 2\end{cases}$$ where $N > 1$. Then
$$\min(M_{i,k}, M_{k,j}) = \begin{cases} 1 & \textrm{ …
- 7,226