Lectures related to Generalized inverse

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

Covers the Moore-Penrose pseudoinverse and its properties for arbitrary matrices.

Explores modular arithmetic, emphasizing inverses and equations in Z/mZ, with practical examples and exercises.

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

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

Covers Cramer's Rule for solving linear equations and calculating matrix inverses.

Covers Cramer's Rule, matrix inverse, determinants, and volume in linear algebra.

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

Explores the Jacobian matrix for geometrically finite elements in the Finite Element Method.

Explores matrix determinant properties, inverse, transpose, and applications in solving equations.

Explores mapping functions, surjections, injective and surjective functions, and bijective functions.

Covers Singular Value Decomposition and Pseudoinverse, explaining their applications in data compression and linear systems.

Explores Cramer's Rule for solving linear equations and calculating matrix inverses.

Covers commutative groups and their significance in cryptography.

Introduces modular arithmetic, its properties, and applications in cryptography and coding theory.

Covers the derivation of the M-step for mu_k and Sigma_k, focusing on key quantities and matrices.

Explores quotients of groups by equivalence relations and the conditions for well-defined sets.

Covers the basics of categories and functors, exploring properties, composition, and uniqueness in category theory.

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