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Results tagged with matrices
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user 484
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.
8
votes
Accepted
Binary matrices with constant row and column sums
So among Hadamard matrices, Sylvester-Hadamard matrices are not special in this regard. … (Most Hadamard matrices do not have this property, but Paley-Hadamard matrices constructed using quadratic residues in $\mathbb{F}_p$, $p\equiv3\pmod{4}$ also do. …
- 2,150
4
votes
Number of unique determinants for an NxN (0,1)-matrix
(Note that the $n$ on the web site refers to $(-1,1)$ matrices, so one should subtract 1 from it if one is talking about $(0,1)$ matrices.) …
- 2,150
9
votes
1
answer
706
views
Automorphisms of a matrix in Smith normal form?
Added: Amritanshu Prasad's answer makes it clear that I am really asking for a description of the group of integer unimodular matrices $P$ such that $D^{-1}PD$ is also integer. … Define $P$ and $Q$ to be the integer unimodular matrices that satisfy $P_2=PP_1$ and $Q_2=Q_1Q$. Then $PDQ=D$. …
- 2,150
9
votes
Maximum determinant of $\{0,1\}$-valued $n\times n$-matrices
As pointed out in Robin Chapman's answer and Frederio Poloni's comment thereto, there is a one-to-one map between normalized $n$-by-$n$ $(-1,1)$ matrices and $(n-1)$-by-$(n-1)$ $(0,1)$ matrices under which … )$ matrices of size $n-1$. …
- 2,150