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Results tagged with linear-algebra
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user 135311
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
26
votes
1
answer
5k
views
Generalization of Cauchy's eigenvalue interlacing theorem?
Cauchy's Interlacing Theorem says that given an $n \times n$ symmetric matrix $A$, let $B$ be an $(n-1) \times (n-1)$ principal submatrix of it, then the eigenvalues of $A$ and those of $B$ interlace. …
- 571
11
votes
3
answers
589
views
Non-singular matrix with restricted entries
Given a set $S$ of integers with $1 \not\in S$, let us consider the set $\mathcal{M}$ of all the symmetric matrices $M$, such that:
All the diagonal entries of $M$ are equal to $1$.
All the off-diag …
- 571
6
votes
0
answers
381
views
Is there an easy way to compute the maximum isotropic subspace over finite fields?
Given a quadratic form (or a symmetric $n \times n$ matrix $A$), an isotropic subspace is a subspace $U$ such that $$U^t A U=0,$$
If I am not mistaken, when the matrix is over reals, the maximum dime …
- 571