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Results tagged with linear-algebra
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user 83122
Questions about the properties of vector spaces and linear transformations, including linear systems in general.
3
votes
Applications of basic linear algebra concepts to computer science?
Spectral graph theory is a big part of theoretical computer science. Some concrete examples are:
1) A big trend in the past decade in TCS has been to utilize the properties of the Laplacian matrix to …
- 763
-1
votes
Inequality for 0-1 matrices
If you allow the entries of $A$ to be in $\{0, \pm 1\}$ then there is a really nice construction that shows that the sum of the entries of $A^{-1}$ can be exponentially large.
Let the diagonals of $ …
- 763
47
votes
3
answers
3k
views
Why is the Vandermonde determinant harmonic?
It can be checked that the Vandermonde determinant defined as
$$V(\alpha_1, \cdots, \alpha_n) = \prod_{1 \le i < j \le n}(\alpha_i-\alpha_j) $$
is a harmonic function, that is $\Delta V = 0$ where $\ …
- 763