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Results tagged with linear-algebra
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user 45255
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
7
votes
1
answer
439
views
How much can I perturb a symmetric stochastic matrix and keep positive solutions?
Suppose $A$ is a symmetric stochastic $n \times n$ matrix with least eigenvalue $\lambda_n>0$. Consider real symmetric perturbations $\widehat{A}$.
How large can I take $\epsilon$ such that $\wideha …
- 1,091
2
votes
1
answer
379
views
Bounding entries of the inverse of certain zero-one matrices
It is known that the entries of the inverse of an (invertible) $n \times n$ zero-one matrix $A$ can grow exponentially in $n$. See this MO question:
Bounding the absolute sum of entries of the invers …
- 1,091
4
votes
Linear algebra proofs in combinatorics?
Variants of the EKR Theorem offer a wide class of examples. This page has a nice list going, by the way.
A friend of mine once made the outrageous claim -- but hear me out -- that most "linear algeb …