Lectures related to Linear Algebra: Matrices and Linear Applications

Explores vector space operations, linear transformations, matrix representation, and linear applications.

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Introduces vector definitions, displacement, addition, and applications in geometry.

Covers translations, homotheties, and geometric transformations using vectors and matrices.

Covers linear transformations, matrices, kernels, and properties of invertible matrices.

Explores the diagonalization of matrices and the conditions for exact diagonalization, with examples demonstrating the process.

Explains the diagonalization of linear transformations using eigenvectors and eigenvalues to form a diagonal matrix.

Covers the reduction of an application, finding reduced forms of matrices, diagonalizability, and polynomial roots.

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

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

Explores the canonical basis in linear algebra, focusing on matrix representation, diagonalizability, and characteristic polynomials.

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

Covers the properties and operations of vector spaces, including addition and scalar multiplication.

Explores matrix representations of linear maps and their invariance, using examples and special cases.

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

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

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

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

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

Covers strategies for matrix operations and the concept of vector spaces.