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数学

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Andrius Kulikauskas

  • ms@ms.lt
  • +370 607 27 665
  • My work is in the Public Domain for all to share freely.

Lietuvių kalba

Introduction E9F5FC

Understandable FFFFFF

Questions FFFFC0

Notes EEEEEE

Software

Book.ElementarySymmetricFunctions istorija

Paslėpti nežymius pakeitimus - Rodyti galutinio teksto pakeitimus

2019 balandžio 17 d., 11:39 atliko AndriusKulikauskas -
Pridėtos 8-11 eilutės:
>>bgcolor=#FFFFC0<<

* What does it mean to multiply together elementary symmetric polynomials?
Pridėtos 29-34 eilutės:

These are inclusion morphisms and they can be composed.

'''Products of polynomials'''

A product of polynomials would yield a pair of possibly overlapping subsets.
2019 balandžio 17 d., 11:27 atliko AndriusKulikauskas -
Pakeistos 23-27 eilutės iš



į:
In other words, given a simplex, these are all the ways of choosing a subsimplex, thus tearing it down, as opposed to building it up.
2019 balandžio 17 d., 11:25 atliko AndriusKulikauskas -
Pridėta 12 eilutė:
* [[https://en.wikipedia.org/wiki/Elementary_symmetric_polynomial | Elementary symmetric polynomial]]
Pakeistos 20-29 eilutės iš
'''Determinant'''
į:
'''Elementary symmetric polynomials'''

There are {$2^n$} terms in all for the elementary symmetric polynomials on {$n$} variables. They express the ways of choosing {$k$} out of {$n$} items for all values of {$k$}. When {$k>n$} then there are no ways.






'''Determinant (Elementary symmetric function of eigenvalues)
'''
2019 balandžio 17 d., 11:13 atliko AndriusKulikauskas -
Pridėta 13 eilutė:
* [[https://en.wikipedia.org/wiki/Schur_functor | Schur functor]]
2019 balandžio 17 d., 10:58 atliko AndriusKulikauskas -
2019 balandžio 17 d., 10:57 atliko AndriusKulikauskas -
Pridėtos 13-16 eilutės:

'''Facts'''

''In representation theory, the exterior algebra is one of the two fundamental Schur functors on the category of vector spaces, the other being the symmetric algebra. Together, these constructions are used to generate the irreducible representations of the general linear group; see fundamental representation.'' ([[https://en.wikipedia.org/wiki/Exterior_algebra | Exterior algebra]])
2019 balandžio 17 d., 10:41 atliko AndriusKulikauskas -
Pridėtos 9-12 eilutės:

'''Readings'''

* [[https://en.wikipedia.org/wiki/Exterior_algebra | Exterior algebra]]
2019 balandžio 17 d., 10:41 atliko AndriusKulikauskas -
Pakeistos 8-12 eilutės iš
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į:
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'''Determinant'''

The determinant is a quintessential geometric value, an n-dimensional volume.
2019 balandžio 17 d., 10:23 atliko AndriusKulikauskas -
Pridėtos 1-8 eilutės:
>>bgcolor=#E9F5FC<<
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[[Symmetric functions in category theory]]

'''What do elementary symmetric functions generate in category theory?'''

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ElementarySymmetricFunctions


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