Lectures related to Untitled | EPFL Graph Search

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.

Matrix Multiplication and Inverses

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

Determinants and Properties

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

Density Operator: Quantum Physics II

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

Numerical Analysis: Direct Methods for Linear Systems

Covers direct methods for solving linear systems in numerical analysis.

Characterization of Invertible Matrices

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

Linear Algebra: Matrices and Linear Applications

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

Linear Algebra: Matrices Properties

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

Singular Value Decomposition: Applications and Interpretation

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

Linear Algebra: Basis and Matrices

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

Calculs and Algorithms for Determinant

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

Matrix Operations: Composition and Product

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

Matrix Equivalence Theorems

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

Matrix Inversion: Basics and Properties

Covers the basics of matrix inversion, properties of matrix multiplication, and the uniqueness of matrix inverses.

Matrix Multiplication: Basics and Properties

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

Matrix Form and IO Analysis

Covers Material Flow Analysis in matrix form and Input-Output Analysis, exploring balance equations, transfer coefficients, GHG emissions, and economic impact.

Density Operator: Matrix to the System State

Explores density operator matrix transformation in quantum physics and the implications of measuring the system, leading to state collapse.

Linear Algebra: Inverse Matrix and Systems Resolution

Covers the concept of inverse matrices and systems resolution, including the conditions for matrix invertibility and the Gauss-Jordan algorithm.

Linear Algebra: Inversion and Uniqueness

Covers matrix inversion and uniqueness in linear algebra, providing examples and verification methods.

Exponential of a Matrix

Explores the exponential of a matrix, properties, Frobenius norm, nilpotent matrices, commutativity, and system solutions.