Advanced linear algebra
Year: 2025
Type: preprint
Abstract: This is an introduction to advanced linear algebra, with emphasis on geometric aspects, and with some applications included too. We first review basic linear algebra, notably with the spectral theorem in its general form, and with the theory of the resultant and discriminant. Then we discuss the Jordan form and its basic applications to physics, and other advanced decomposition results for the matrices. We then go into positivity topics, involving matrices and bilinear forms, and with a look into curved space-time, and discrete Laplacians. Finally, we discuss the various groups of matrices, with a look at reflection groups, Lie groups, spin matrices and random matrices.
Source: arXiv (Cornell University)
Author: Banica, Teo
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W6966801443
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