Applications of linear algebra other than Euclidean vector spaces.

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A typical example of finite-dimensional vector space is Euclidean space $mathbbR^n$, 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 $mathbbR^n$?




linear-algebra soft-question motivation




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    Markov chains...of the top of my head.
    – Pi_die_die
    Jul 25 at 5:15






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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: en.wikipedia.org/wiki/Spectral_graph_theory. (On a more advanced level, there are homology/cohomology vector spaces.)
    – Lorenzo
    Jul 25 at 5:31











  • linear error-correcting codes?
    – Lord Shark the Unknown
    Jul 25 at 5:37














up vote
0
down vote

favorite












A typical example of finite-dimensional vector space is Euclidean space $mathbbR^n$, 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 $mathbbR^n$?




linear-algebra soft-question motivation




share|cite|improve this question















  • 1




    Markov chains...of the top of my head.
    – Pi_die_die
    Jul 25 at 5:15






  • 1




    $F_2^n$ (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: en.wikipedia.org/wiki/Spectral_graph_theory. (On a more advanced level, there are homology/cohomology vector spaces.)
    – Lorenzo
    Jul 25 at 5:31











  • linear error-correcting codes?
    – Lord Shark the Unknown
    Jul 25 at 5:37












up vote
0
down vote

favorite









up vote
0
down vote

favorite











A typical example of finite-dimensional vector space is Euclidean space $mathbbR^n$, 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 $mathbbR^n$?




linear-algebra soft-question motivation




share|cite|improve this question











A typical example of finite-dimensional vector space is Euclidean space $mathbbR^n$, 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 $mathbbR^n$?





linear-algebra soft-question motivation





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 25 at 5:12









marimo

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  • 1




    Markov chains...of the top of my head.
    – Pi_die_die
    Jul 25 at 5:15






  • 1




    $F_2^n$ (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: en.wikipedia.org/wiki/Spectral_graph_theory. (On a more advanced level, there are homology/cohomology vector spaces.)
    – Lorenzo
    Jul 25 at 5:31











  • linear error-correcting codes?
    – Lord Shark the Unknown
    Jul 25 at 5:37












  • 1




    Markov chains...of the top of my head.
    – Pi_die_die
    Jul 25 at 5:15






  • 1




    $F_2^n$ (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: en.wikipedia.org/wiki/Spectral_graph_theory. (On a more advanced level, there are homology/cohomology vector spaces.)
    – Lorenzo
    Jul 25 at 5:31











  • linear error-correcting codes?
    – Lord Shark the Unknown
    Jul 25 at 5:37







1




1




Markov chains...of the top of my head.
– Pi_die_die
Jul 25 at 5:15




Markov chains...of the top of my head.
– Pi_die_die
Jul 25 at 5:15




1




1




$F_2^n$ (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: en.wikipedia.org/wiki/Spectral_graph_theory. (On a more advanced level, there are homology/cohomology vector spaces.)
– Lorenzo
Jul 25 at 5:31





$F_2^n$ (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: en.wikipedia.org/wiki/Spectral_graph_theory. (On a more advanced level, there are homology/cohomology vector spaces.)
– Lorenzo
Jul 25 at 5:31













linear error-correcting codes?
– Lord Shark the Unknown
Jul 25 at 5:37




linear error-correcting codes?
– Lord Shark the Unknown
Jul 25 at 5:37















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