Lectures related to Matrix Calculus

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

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

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

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

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

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

Covers the matrix representations of linear applications and the equivalence between matrices.

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

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

Covers the matrix representations of linear applications and how to find representative matrices.

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

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

Covers matrix multiplication, properties, and the identity matrix in algebraic operations.

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

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

Covers the diagonalization of linear transformations in R^3, exploring properties and examples.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

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

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

Covers matrix calculus, including determinants, matrix inversion, and solutions to systems of linear equations.