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Results tagged with matrices
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user 27513
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
Cardinality of the maximum points of the determinant on matrices with entries in [-1, 1]
For orders $n \equiv 0 \bmod 4$ the optimal Gram matrix is $nI_{n}$ and the maximal determinant matrices are Hadamard matrices. … When the optimal Gram matrices are known and attained, the number of solutions will be finite. For orders $3 \bmod 4$ there are not even conjectures for what the optimal Gram matrices should be. …
- 1,300
8
votes
Are these two methods for constructing Hadamard matrices known?
I think it very probably that your matrices are Hadamard equivalent to the Sylvester matrices. … Then this looks a lot like the construction of Sylvester matrices given in Section 2.1.1 of Horadam's Hadamard matrices and their applications. …
- 1,300
1
vote
Accepted
Under row operations and column permutations a matrix A can be put in the non-unique form ( ...
Let $A$ be an $n \times m$ matrix over $k$. Since the group $\textrm{GL}_{n}(k)$ acts transitively on the ordered bases of an $n$-dimensional $k$-vector space, any $n$ linearly independent columns of …
- 1,300
4
votes
Accepted
For which finite projective planes can the incidence structure be written as a circulant mat...
in the first row of the incidence matrix with elements of the cyclic group of order $v$, then allowing the automorphism group of this cyclic group to act in the natural way gives different incidence matrices … A single plane could have multiple inequivalent realisations as a difference set, these will give further realisations as circulant incidence matrices. …
- 1,300
5
votes
Accepted
What is the mathematician's definition of the determinant?
From this axiomatic starting point, the proof that the determinant is multiplicative is lengthy, and depends on rank deficient matrices having zero determinant and on the general linear group being generated … by elementary matrices, etc. …
- 1,300