Difference between revisions of "Video/What is...representation theory?"
Jump to navigation
Jump to search
| (6 intermediate revisions by 2 users not shown) | |||
| Line 11: | Line 11: | ||
<noinclude> | <noinclude> | ||
{{# | {{#Widget:YouTube | ||
|VYzhA_nj0sU | |id=VYzhA_nj0sU | ||
}} | }} | ||
| Line 18: | Line 18: | ||
# [[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= | ||
| Line 23: | Line 24: | ||
...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 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 [https://youtu.be/VYzhA_nj0sU?t=970 here]. | ||
{{#widget:YouTube | |||
== | |id=VYzhA_nj0sU | ||
[[Organized by::VisualMath]] | |width=640 | ||
}} | |||
[[ | |||
{{PagePostfix | |||
|category_csd=Representation Theory,Linear Algebra,Data Science,Approximation | |||
|semantic_labels=Organized by:[[Organized by::VisualMath]] Presented by:[[Presented by::Daniel Tubbenhauer]] | |||
}} | |||
</noinclude> | </noinclude> | ||
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:
- Analysis and Control of Boolean Networks A Semi-tensor Product Approach[1]
- A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES[2]
- 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
- ↑ 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.
- ↑ Rushdi, Ali Muhammad; Ghaleb, Fares (August 28, 2017). "A BRIEF TUTORIAL EXPOSITION OF SEMI-TENSOR PRODUCTS OF MATRICES". local page: Research Gate.
- ↑ zamzawed, ed. (Aug 15, 2022). What's a representation? An intro to modern math's magical machinery. local page: zamzawed.
- ↑ Burnside, William (1897). Theory of Groups of Finite Order. local page: Cambridge University Press.
Related Pages
Organized by:VisualMath Presented by:Daniel Tubbenhauer