Concept

Special linear group

Related lectures (28)

Explores the torus, linear groups, stability properties of matrices, and homomorphisms.

Dynamics on Homogeneous Spaces and Interactions with Number Theory

Explores dynamics on homogeneous spaces and their interactions with number theory, focusing on modular lattices and the Iwasawa decomposition theorem.

Linear algebraic groups

Covers linear algebraic groups, including special sets and matrix examples.

Linear Projective Groups

Explores linear projective groups, quaternions, subgroup generation, and normality.

Symplectic Groups

Explores symplectic groups, linear transformations preserving non-degenerate alternating bilinear forms on vector spaces.

Self-similar groups II

Explores self-similar groups acting on rooted trees and their properties.

Determinants: Special Linear Groups and Matrix Properties

Explores the special linear group, matrix properties, and determinant theorems.

Group Actions on Lattices

Explores group actions on lattices, emphasizing GL₂(Q) and GL₂(Ag) compatibility and alternative formulations.

Group Actions: Examples

Showcases examples of group actions on vector spaces and topological spaces.

Matrix Operations: Scaling and Invertibility

Covers scaled matrices, ladder matrices, and the Gauss method for matrix operations.

Spectral Analysis: Hyperbolic Surfaces

Explores the spectral analysis of hyperbolic surfaces through the trace formula and its applications in understanding geometric and spectral properties.

Linear Algebra: Elementary Row Operations

Covers elementary row operations, equivalent matrices, invertibility, and bases in linear algebra.

Density matrix: statistical mixtures

Covers the concept of density matrix and statistical mixtures in quantum mechanics, explaining how to measure observables and calculate averages.

Lie Algebra: Representations

Explores Lie algebra representations, emphasizing SU(2) and traceless matrices, explained by Alfredo Glioti.

Tutorial On Auto-encoders

Explores auto-encoders, covering invertibility conditions, projections, and generalized inverses in linear algebra.

Truncated CG: Conjugate Gradients

Covers the truncated conjugate gradients algorithm for solving positive definite linear maps iteratively.

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Vector Fields and Lorentz Tensors: Representation Theory

Covers the transformation properties of vector fields and their representation in Lorentz tensors.

Representation of SL2Z

Delves into the representation of SL2Z and the function F, exploring its transformation properties and relation to modular forms.

Matrix Inversion

Explores matrix inversion, conditions for invertibility, uniqueness of the inverse, and elementary matrices for inversion.