Difference between revisions of "Video/What is...representation theory?"

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# [[Book/Analysis and Control of Boolean Networks A Semi-tensor Product Approach|Analysis and Control of Boolean Networks A Semi-tensor Product Approach]]<ref>{{:Book/Analysis and Control of Boolean Networks A Semi-tensor Product Approach}}</ref>
# [[Book/Analysis and Control of Boolean Networks A Semi-tensor Product Approach|Analysis and Control of Boolean Networks A Semi-tensor Product Approach]]<ref>{{:Book/Analysis and Control of Boolean Networks A Semi-tensor Product Approach}}</ref>
# [[Paper/A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES|A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES]]<ref>{{:Paper/A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES}}</ref>
# [[Paper/A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES|A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES]]<ref>{{:Paper/A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES}}</ref>
# [[Video/What's a representation? An intro to modern math's magical machinery|What's a representation? An intro to modern math's magical machinery]]<ref>{{:Video/What's a representation? An intro to modern math's magical machinery}}</ref>


=Theory of Groups of Finite Order=
=Theory of Groups of Finite Order=
The end of this video extensively discusses the idea of [[William Burnside]]'s work on [[Book/Theory of Groups of Finite Order|Theory of Groups of Finite Order]]<ref>{{:Book/Theory of Groups of Finite Order}}</ref>.
The end of this video extensively discusses the idea of [[William Burnside]]'s work on [[Book/Theory of Groups of Finite Order|Theory of Groups of Finite Order]]<ref>{{:Book/Theory of Groups of Finite Order}}</ref>. The critical message can be summarized in the second version (published in 1911, which stated the following message:
...it is now '''more true''' to say that for further advances in the abstract theory one must look largely to the representation of a group as a group of linear substitutions.


=References=
It would be useful to watch the video from [https://youtu.be/VYzhA_nj0sU?t=970 here].
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[[Category:Linear Algebra]]
 
[[Category:Data Science]]
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[[Category:Approximation]]
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|semantic_labels=Organized by:[[Organized by::VisualMath]] Presented by:[[Presented by::Daniel Tubbenhauer]]
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Latest revision as of 01:48, 5 January 2023

Tubbenhauer, Daniel (Mar 30, 2022). What is...representation theory?. local page: VisualMath. 


According to this video, the main thesis of Representation Theory is the linear approximation of algebraic objects. It would be useful to refer to the Semi-tensor product(STP) as developed by Daizhan Cheng. See following references:

  1. Analysis and Control of Boolean Networks A Semi-tensor Product Approach[1]
  2. A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES[2]
  3. What's a representation? An intro to modern math's magical machinery[3]

Theory of Groups of Finite Order

The end of this video extensively discusses the idea of William Burnside's work on Theory of Groups of Finite Order[4]. The critical message can be summarized in the second version (published in 1911, which stated the following message: 

...it is now more true to say that for further advances in the abstract theory one must look largely to the representation of a group as a group of linear substitutions.

It would be useful to watch the video from here.

References

  1. ↑ Cheng, Daizhan; Qi, Hongsheng; Li, Zhiqiang (2011). Analysis and Control of Boolean Networks:A Semi-tensor Product Approach. local page: Springer-Verlag. ISBN 978-0-85729-097-7. 
  2. ↑ Rushdi, Ali Muhammad; Ghaleb, Fares (August 28, 2017). "A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES". local page: Research Gate. 
  3. ↑ zamzawed, ed. (Aug 15, 2022). What's a representation? An intro to modern math's magical machinery. local page: zamzawed. 
  4. ↑ Burnside, William (1897). Theory of Groups of Finite Order. local page: Cambridge University Press. 

Related Pages

Organized by:VisualMath Presented by:Daniel Tubbenhauer


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