Lectures related to Characterization of totally unimodular matrices

Eigenstate Thermalization Hypothesis

Explores the Eigenstate Thermalization Hypothesis in quantum systems, emphasizing the random matrix theory and the behavior of observables in thermal equilibrium.

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Matrix Operations: LU Factorization & Subspace Vector

Covers LU factorization, determinants, subspaces, and matrix products.

Linear Algebra: Matrices and Linear Applications

Covers matrices, linear applications, vector spaces, and bijective functions.

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Calculs and Algorithms for Determinant

Covers calculations and algorithms for determining the determinant of a matrix, including permuting rows and multiplying by coefficients.

Strategies for Determinant Calculation

Covers strategies for calculating determinants and their geometric interpretation in various dimensions.

Linear Algebra: Determinants and Applications

Explores determinants, similarity invariance, Cramer's formula, and geometric interpretations in matrices.

Matrix of Cofactors and Inverse Matrix Formula

Covers the concept of the matrix of cofactors and a formula to calculate the inverse of a matrix.

Linear Algebra: Matrix Representation

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Elementary Matrices and Inverses

Covers elementary matrices, their properties, and the algorithm to find the inverse of a matrix.

Matrix Multiplication and Inverses

Covers matrix product, inverses, and properties of invertible matrices.

Characterization of Invertible Matrices

Explores the properties of invertible matrices, including unique solutions and linear independence.

Determinants and Properties

Covers the definition and properties of determinants, including the rule of Sarrus for 3x3 matrices.

Matrices: Elementary Linear Algebra

Explores elementary linear algebra concepts related to matrices, including invertible connections and matrix rank.

Matrix Operations: Inverse and Reduction to Echelon Form

Covers matrix operations and reduction to echelon form with practical examples.

Linear Algebra: Matrices Properties

Explores properties of 3x3 matrices with real coefficients and determinant calculation methods.

Matrix Determinants: Properties and Calculations

Covers the properties and calculations of matrix determinants, including triangular matrices and elementary row operations.

Matrix Equivalence Theorems

Explores matrix equivalence theorems for systems of equations and least squares solutions.

Matrix Inversion

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