Lectures related to Involutory matrix

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.

Matrix Operations: Properties and Applications

Covers the properties and applications of matrix operations and their convergence in series.

Elementary Matrices and Inverses

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

Matrix Equation Resolution

Covers the resolution of a system of equations using the Gramer rule.

Determinants Calculation

Covers the calculation of determinants and determining matrix invertibility based on parameter values.

Matrix Invertibility

Explores matrix invertibility and unique solutions in linear systems through row operations.

Optimization with Constraints: KKT Conditions

Covers optimization with constraints using KKT conditions and matrix invertibility in numerical analysis.

Matrix Invertibility

Covers the proof of the invertibility of a matrix by showing that the transpose of the matrix multiplied by itself results in an identity matrix.

Linear Algebra Basics

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

Non-Diagonalizable Case: Triple Eigenvalue

Explores the scenarios of a matrix with a triple eigenvalue and its basis representation in R^3.

Matrix Operations: Definitions and Properties

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

Linear Algebra: Matrices Properties

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

Linear Algebra: Main Theorem and Injectivity

Covers the main theorem of linear algebra and the conditions for injectivity.

Ker A = Ker (ATA)

Explores the equality between Ker A and Ker (ATA) in linear algebra.

Eigenvalues Reduction: Two Real Eigenvalues

Explores the reduction of a matrix based on its eigenvalues, focusing on the case of two real eigenvalues.

Matrix Equations: Finding Free Variables

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

Invertibility Criteria and Inverse Calculation

Explores the criterion for matrix invertibility and the calculation of the inverse.

Canonical Transformations: Symplectic Group and Properties

Explores canonical transformations, symplectic groups, real matrices, preserved quantities, and volumes in phase space.

Linear Regression Testing

Explores least squares in linear regression, hypothesis testing, outliers, and model assumptions.

Matrix Similarity and Diagonalization

Explores matrix similarity, diagonalization, characteristic polynomials, eigenvalues, and eigenvectors in linear algebra.