Linear algebra and group theory - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

Linear algebra and group theory

Teo Banica
  • Fonction : Auteur
  • PersonId : 1045618

Résumé

This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure, and more, and with the determinant being constructed as it should, as a signed volume. We discuss then the basic applications of linear algebra to questions in analysis. Then we get into the study of the closed groups of unitary matrices $G\subset U_N$, with some basic algebraic theory, and with a number of probability computations, in the finite group case. In the general case, where $G\subset U_N$ is compact, we explain how the Weingarten integration formula works, and we present some basic $N\to\infty$ applications.
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Dates et versions

hal-03698729 , version 1 (18-06-2022)
hal-03698729 , version 2 (11-10-2022)
hal-03698729 , version 3 (04-02-2023)
hal-03698729 , version 4 (14-04-2023)
hal-03698729 , version 5 (29-07-2024)

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  • HAL Id : hal-03698729 , version 2

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Teo Banica. Linear algebra and group theory. 2022. ⟨hal-03698729v2⟩
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