Concept

Matrix (mathematics)

Related lectures (29)

Linear Algebra: Matrices and Operations

Introduces key concepts in linear algebra, including matrices, operations, and numerical invariants.

Elementary Matrices and Inverses

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

Matrix Equations: Finding Free Variables

Explains how to find free variables in matrix equations and analyze characteristic polynomials.

Matrix Multiplication: Applications and Properties

Covers matrix multiplication, properties, and inverses in linear algebra.

Asymptotic States and S-matrix

Covers the concept of asymptotic states and S-matrix in quantum field theory, focusing on the evolution of wave packets and the scattering states.

Linear Algebra Basics

Covers fundamental concepts in linear algebra, including linear equations, matrix operations, determinants, and vector spaces.

Linear Algebra: Matrix Operations

Explores the equivalence between different properties of linear transformations represented by matrices and various matrix operations.

Linear Algebra: Matrices and Inverses

Explores matrices, inverses, and their applications in linear algebra, emphasizing composition and transformation properties.

Matrix Representations of Linear Applications

Explores matrix representations of linear applications, including change of basis and invariants.

Asymptotic States and S-matrix: Operators

Explores asymptotic states, S-matrix, and operators in quantum field theory, emphasizing the role of discrete symmetries and complete sets of states.

Characteristic Polynomials and Similar Matrices

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

Asymptotic States and S-matrix

Explores asymptotic states, S-matrix, Lippmann-Schwinger equation, and energy robustness in quantum field theory.

Linear Equations and Matrix Calculations

Covers the fundamentals of linear equations, matrices, and systems of linear equations, including matrix operations and solutions.

Matrix Operations: Inverse and Reduction to Echelon Form

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

Matrix Calculus

Covers the definition and basic operations of matrices, including addition, scalar multiplication, and matrix multiplication.

Matrix Operations: Composition and Product

Covers the composition and product of matrices, including matrix multiplication.

Eigenstate Thermalization Hypothesis

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

Matrix Operations: LU Factorization & Subspace Vector

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

Matrix Equations and Homogeneous Systems

Explores matrix equations, homogeneous systems, solutions, consistency, and properties.

Discrete Symmetries: Asymptotic States and S-matrix

Covers the concept of discrete symmetries, focusing on the introduction to asymptotic states and S-matrix.