Applications of linear algebra other than Euclidean vector spaces.

Asked Jul 25 '18 at 05:12

Active Sep 24 '20 at 08:00

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A typical example of finite-dimensional vector space is Euclidean space $\mathbb{R}^n$, but there are other type of it. For example, the space of polynomials whose order is less than $n$, the space of solutions of a linear differential equation, etc...

Are there interesting application of linear algebra to a space other than $\mathbb{R}^n$?

edited Sep 24 '20 at 08:00

Martin Sleziak

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asked Jul 25 '18 at 05:12

marimo

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Markov chains...of the top of my head. – Pi_die_die Jul 25 '18 at 05:15
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$F_2^n$ (vector spaces over finite fields) for coding theory, or for applications in graph theory and algorithms. The space of complex valued function on the vertices of a graph is another important one, especially for spectral graph theory: https://en.wikipedia.org/wiki/Spectral_graph_theory. (On a more advanced level, there are homology/cohomology vector spaces.) – Elle Najt Jul 25 '18 at 05:31
linear error-correcting codes? – Angina Seng Jul 25 '18 at 05:37
A bit related question on MathOverflow: Elementary applications of linear algebra over finite fields. Some related questions on this site: Uses of vector spaces over $\mathbb Q$, Real life applications of general vector spaces, How does linear algebra help with computer science?, Applications of real numbers being a vector space over the rational numbers. – Martin Sleziak Sep 24 '20 at 08:02

Applications of linear algebra other than Euclidean vector spaces.

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