Lectures related to Linear Transformations: Matrices and Applications

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Delves into the bijection between linear applications and matrices, exploring linearity, injectivity, surjectivity, and the consequences of this relationship.

Linear Applications: Bases and Dependencies

Explores forming bases, dependencies, and relationships in linear applications using invertible matrices and canonical bases.

Linear Algebra: Matrices Properties

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

Matrix Operations: Composition and Product

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

Eigenvalues and Eigenvectors in 3D

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Eigenvalues and Similar Matrices

Introduces eigenvalues, eigenvectors, and similar matrices, emphasizing diagonalization and geometric interpretations.