Real-world applications of fields, rings and groups in linear algebra.
$begingroup$
Real-world applications of fields, rings and groups in linear algebra.
A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact that I could only mention cyber security - nothing more (I'm studying IT). That's why I would like to get some more detailed suggestions. I would really appreciate that.
Thank you in advance!
linear-algebra abstract-algebra group-theory field-theory applications
edited 1 hour ago
Bernard
125k743119
asked 1 hour ago
DoesbaddelDoesbaddel
36113
$endgroup$
add a comment |
$begingroup$
Real-world applications of fields, rings and groups in linear algebra.
A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact that I could only mention cyber security - nothing more (I'm studying IT). That's why I would like to get some more detailed suggestions. I would really appreciate that.
Thank you in advance!
linear-algebra abstract-algebra group-theory field-theory applications
edited 1 hour ago
Bernard
125k743119
asked 1 hour ago
DoesbaddelDoesbaddel
36113
$endgroup$
3
$begingroup$
There is a lot of linear-algebraic group theory in quantum mechanics. See this wiki page for instance
$endgroup$
– Omnomnomnom
1 hour ago
3
$begingroup$
I'm no expert, but I'm lead to believe that plenty of the tests in chemistry to detect various molecules work by examining symmetry groups.
$endgroup$
– Theo Bendit
1 hour ago
2
$begingroup$
Counting theorem is a good one-see also math.stackexchange.com/questions/324253/…
$endgroup$
– John_dydx
1 hour ago
add a comment |
$begingroup$
Real-world applications of fields, rings and groups in linear algebra.
A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact that I could only mention cyber security - nothing more (I'm studying IT). That's why I would like to get some more detailed suggestions. I would really appreciate that.
Thank you in advance!
linear-algebra abstract-algebra group-theory field-theory applications
edited 1 hour ago
Bernard
125k743119
asked 1 hour ago
DoesbaddelDoesbaddel
36113
$endgroup$
Real-world applications of fields, rings and groups in linear algebra.
A friend of mine asked me where one could use the definitions of rings, groups, fields etc. I was very embarrassed of the fact that I could only mention cyber security - nothing more (I'm studying IT). That's why I would like to get some more detailed suggestions. I would really appreciate that.
Thank you in advance!
linear-algebra abstract-algebra group-theory field-theory applications
linear-algebra abstract-algebra group-theory field-theory applications
edited 1 hour ago
Bernard
125k743119
asked 1 hour ago
DoesbaddelDoesbaddel
36113
edited 1 hour ago
Bernard
125k743119
asked 1 hour ago
DoesbaddelDoesbaddel
36113
edited 1 hour ago
Bernard
125k743119
edited 1 hour ago
Bernard
125k743119
edited 1 hour ago
Bernard
125k743119
125k743119
asked 1 hour ago
DoesbaddelDoesbaddel
36113
asked 1 hour ago
DoesbaddelDoesbaddel
36113
asked 1 hour ago
DoesbaddelDoesbaddel
36113
36113
3
$begingroup$
There is a lot of linear-algebraic group theory in quantum mechanics. See this wiki page for instance
$endgroup$
– Omnomnomnom
1 hour ago
3
$begingroup$
I'm no expert, but I'm lead to believe that plenty of the tests in chemistry to detect various molecules work by examining symmetry groups.
$endgroup$
– Theo Bendit
1 hour ago
2
$begingroup$
Counting theorem is a good one-see also math.stackexchange.com/questions/324253/…
$endgroup$
– John_dydx
1 hour ago
add a comment |
3
$begingroup$
There is a lot of linear-algebraic group theory in quantum mechanics. See this wiki page for instance
$endgroup$
– Omnomnomnom
1 hour ago
3
$begingroup$
I'm no expert, but I'm lead to believe that plenty of the tests in chemistry to detect various molecules work by examining symmetry groups.
$endgroup$
– Theo Bendit
1 hour ago
2
$begingroup$
Counting theorem is a good one-see also math.stackexchange.com/questions/324253/…
$endgroup$
– John_dydx
1 hour ago
3
3
$begingroup$
There is a lot of linear-algebraic group theory in quantum mechanics. See this wiki page for instance
$endgroup$
– Omnomnomnom
1 hour ago
$begingroup$
There is a lot of linear-algebraic group theory in quantum mechanics. See this wiki page for instance
$endgroup$
– Omnomnomnom
1 hour ago
3
3
$begingroup$
I'm no expert, but I'm lead to believe that plenty of the tests in chemistry to detect various molecules work by examining symmetry groups.
$endgroup$
– Theo Bendit
1 hour ago
$begingroup$
I'm no expert, but I'm lead to believe that plenty of the tests in chemistry to detect various molecules work by examining symmetry groups.
$endgroup$
– Theo Bendit
1 hour ago
2
2
$begingroup$
Counting theorem is a good one-see also math.stackexchange.com/questions/324253/…
$endgroup$
– John_dydx
1 hour ago
$begingroup$
Counting theorem is a good one-see also math.stackexchange.com/questions/324253/…
$endgroup$
– John_dydx
1 hour ago
add a comment |
2 Answers
2
active
oldest
votes
$begingroup$
Well, I'd consider the brand new book from Gilbert Strang: ''Linear Algebra and Learning from Data'', Cambridge Univ. Press, 2018. His learning from data culminates into the construction of deep neural networks.
Another application besides cryptography is coding theory, where finite fields are used to define linear codes. There is also a decent generalization to linear codes over the ring of integers modulo 4, which give rises by the Gray map to nonlinear binary codes which are better than any linear code with the same block length.
answered 1 hour ago
WuestenfuxWuestenfux
5,8001513
$endgroup$
add a comment |
$begingroup$
There's the GraphBLAS project [0] which is for graph algorithms expressed as linear algebra (see also [1]). It turns out that many such algorithms can be done this way if you change the semiring over which the matrices live. See for example this TOMS pre-print [2].
[0] http://graphblas.org
[1] Graph Algorithms in the Language of Linear Algebra, Kepner&Gilbert(ed), https://epubs.siam.org/doi/book/10.1137/1.9780898719918
[2] http://faculty.cse.tamu.edu/davis/GraphBLAS_files/toms_graphblas.pdf
answered 29 mins ago
JCKJCK
111
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add a comment |
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2 Answers
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active
oldest
votes
2 Answers
2
active
oldest
votes
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active
oldest
votes
$begingroup$
Well, I'd consider the brand new book from Gilbert Strang: ''Linear Algebra and Learning from Data'', Cambridge Univ. Press, 2018. His learning from data culminates into the construction of deep neural networks.
Another application besides cryptography is coding theory, where finite fields are used to define linear codes. There is also a decent generalization to linear codes over the ring of integers modulo 4, which give rises by the Gray map to nonlinear binary codes which are better than any linear code with the same block length.
answered 1 hour ago
WuestenfuxWuestenfux
5,8001513
$endgroup$
add a comment |
$begingroup$
Well, I'd consider the brand new book from Gilbert Strang: ''Linear Algebra and Learning from Data'', Cambridge Univ. Press, 2018. His learning from data culminates into the construction of deep neural networks.
Another application besides cryptography is coding theory, where finite fields are used to define linear codes. There is also a decent generalization to linear codes over the ring of integers modulo 4, which give rises by the Gray map to nonlinear binary codes which are better than any linear code with the same block length.
answered 1 hour ago
WuestenfuxWuestenfux
5,8001513
$endgroup$
add a comment |
$begingroup$
Well, I'd consider the brand new book from Gilbert Strang: ''Linear Algebra and Learning from Data'', Cambridge Univ. Press, 2018. His learning from data culminates into the construction of deep neural networks.
Another application besides cryptography is coding theory, where finite fields are used to define linear codes. There is also a decent generalization to linear codes over the ring of integers modulo 4, which give rises by the Gray map to nonlinear binary codes which are better than any linear code with the same block length.
answered 1 hour ago
WuestenfuxWuestenfux
5,8001513
$endgroup$
Well, I'd consider the brand new book from Gilbert Strang: ''Linear Algebra and Learning from Data'', Cambridge Univ. Press, 2018. His learning from data culminates into the construction of deep neural networks.
Another application besides cryptography is coding theory, where finite fields are used to define linear codes. There is also a decent generalization to linear codes over the ring of integers modulo 4, which give rises by the Gray map to nonlinear binary codes which are better than any linear code with the same block length.
answered 1 hour ago
WuestenfuxWuestenfux
5,8001513
answered 1 hour ago
WuestenfuxWuestenfux
5,8001513
answered 1 hour ago
WuestenfuxWuestenfux
5,8001513
answered 1 hour ago
WuestenfuxWuestenfux
5,8001513
5,8001513
add a comment |
add a comment |
$begingroup$
There's the GraphBLAS project [0] which is for graph algorithms expressed as linear algebra (see also [1]). It turns out that many such algorithms can be done this way if you change the semiring over which the matrices live. See for example this TOMS pre-print [2].
[0] http://graphblas.org
[1] Graph Algorithms in the Language of Linear Algebra, Kepner&Gilbert(ed), https://epubs.siam.org/doi/book/10.1137/1.9780898719918
[2] http://faculty.cse.tamu.edu/davis/GraphBLAS_files/toms_graphblas.pdf
answered 29 mins ago
JCKJCK
111
$endgroup$
add a comment |
$begingroup$
There's the GraphBLAS project [0] which is for graph algorithms expressed as linear algebra (see also [1]). It turns out that many such algorithms can be done this way if you change the semiring over which the matrices live. See for example this TOMS pre-print [2].
[0] http://graphblas.org
[1] Graph Algorithms in the Language of Linear Algebra, Kepner&Gilbert(ed), https://epubs.siam.org/doi/book/10.1137/1.9780898719918
[2] http://faculty.cse.tamu.edu/davis/GraphBLAS_files/toms_graphblas.pdf
answered 29 mins ago
JCKJCK
111
$endgroup$
add a comment |
$begingroup$
There's the GraphBLAS project [0] which is for graph algorithms expressed as linear algebra (see also [1]). It turns out that many such algorithms can be done this way if you change the semiring over which the matrices live. See for example this TOMS pre-print [2].
[0] http://graphblas.org
[1] Graph Algorithms in the Language of Linear Algebra, Kepner&Gilbert(ed), https://epubs.siam.org/doi/book/10.1137/1.9780898719918
[2] http://faculty.cse.tamu.edu/davis/GraphBLAS_files/toms_graphblas.pdf
answered 29 mins ago
JCKJCK
111
$endgroup$
There's the GraphBLAS project [0] which is for graph algorithms expressed as linear algebra (see also [1]). It turns out that many such algorithms can be done this way if you change the semiring over which the matrices live. See for example this TOMS pre-print [2].
[0] http://graphblas.org
[1] Graph Algorithms in the Language of Linear Algebra, Kepner&Gilbert(ed), https://epubs.siam.org/doi/book/10.1137/1.9780898719918
[2] http://faculty.cse.tamu.edu/davis/GraphBLAS_files/toms_graphblas.pdf
answered 29 mins ago
JCKJCK
111
answered 29 mins ago
JCKJCK
111
answered 29 mins ago
JCKJCK
111
answered 29 mins ago
JCKJCK
111
111
add a comment |
add a comment |
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3
$begingroup$
There is a lot of linear-algebraic group theory in quantum mechanics. See this wiki page for instance
$endgroup$
– Omnomnomnom
1 hour ago
3
$begingroup$
I'm no expert, but I'm lead to believe that plenty of the tests in chemistry to detect various molecules work by examining symmetry groups.
$endgroup$
– Theo Bendit
1 hour ago
2
$begingroup$
Counting theorem is a good one-see also math.stackexchange.com/questions/324253/…
$endgroup$
– John_dydx
1 hour ago