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Linear Algebra: Matrices Properties

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

Determinants and Properties

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

Characteristic Polynomials and Similar Matrices

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

Determinant: Definitions and Examples

Covers the definition of the determinant of a matrix and provides examples for calculation.

Matrix Operations: Definitions and Properties

Covers the definitions and properties of matrices, including matrix operations and determinants.

Linear Algebra: Matrices and Linear Applications

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

Calculs and Algorithms for Determinant

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

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

Matrix Operations: Product and Inverse

Covers matrix operations, focusing on the product and inverse of matrices.

Alternative Definitions of Determinant

Explores alternative definitions of determinants, properties of matrices, geometric interpretations, and the Gauss algorithm.

Matrix Operations: LU Factorization & Subspace Vector

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

Characterization of Invertible Matrices

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

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.

Density Operator: Quantum Physics II

Covers the concept of matrix to the density operator in quantum physics.

Matrix Operations: Inverse and Reduction to Echelon Form

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

Matrix Multiplication: Basics and Properties

Covers the basics of matrix multiplication, including properties and examples.

Triangular Block Matrices

Explores upper triangular block matrices, invertibility, elementary transformations, and determinants with examples.

Linear Algebra: Basis and Matrices

Covers the concept of basis, linear transformations, matrices, inverses, determinants, and bijective transformations.

Eigenstate Thermalization Hypothesis

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

Row-echelon and reduced row-echelon matrices

Explains row-echelon and reduced row-echelon matrices and their role in simplifying system resolution.