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Results tagged with linear-algebra
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user 484
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
2
votes
Extremal properties of the determinant for matrices with entries in a fixed subset of $[-1,1...
I don't know the answer to your question, but the following is a bit long for a comment.
We can always assume one of the matrix elements is 1 since rescaling all elements so that the largest element …
- 2,150
2
votes
Defining a canonical ordering of matrix rows/columns
Although, as Peter Shor indicated, graph isomorphism is a difficult computational problem, people have devised algorithms that work well in many practical situations. One example is Brendan McKay's n …
- 2,150
4
votes
Number of unique determinants for an NxN (0,1)-matrix
From Hadamard's bound the largest possible determinant of an $n\times n$ (0,1) matrix is $h_n=2^{-n}(n+1)^{(n+1)/2}$. The data at http://www.indiana.edu/~maxdet/spectrum.html suggest several conject …
- 2,150
5
votes
[Matrices over Z] - An algorithm for calculating the diagonal with elementary operations
At Scott's request, here's my comment in answer form:
The stated conditions imply imply that your two matrices are equivalent. Up to permutation of rows and columns, your diagonal matrix is the Smit …
- 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 …
- 2,150