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Questions about the properties of vector spaces and linear transformations, including linear systems in general.

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 $\ …
Sandeep Silwal's user avatar
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 …
Sandeep Silwal's user avatar
-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 $ …
Sandeep Silwal's user avatar