How is linear algebra used in algorithms?

Question

Several of my peers have mentioned that \"linear algebra\" is very important when studying algorithms. I\'ve studied a variety of algorithms and taken a few linear algebra cour

Answer 1

For example what interesting things can one with a connectivity matrix for a graph?

A lot of algebraic properties of the matrix are invariant under permutations of vertices (for example abs(determinant)), so if two graphs are isomorphic, their values will be equal.

This is a source for good heuristics for determining whether two graphs are not isomorphic, since of course equality does not guarantee existance of isomorphism.

Check algebraic graph theory for a lot of other interesting techniques.