Lectures related to Reducing an Application

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

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

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

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

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

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

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

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.

Explains the diagonalization of matrices, criteria, and significance of distinct eigenvalues.

Covers the reduction of a linear transformation in a 2-dimensional space to find a simpler matrix representation.

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

Covers the reduction of a linear application and finding corresponding reduced forms and bases.

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

Explores canonical basis, linear mapping, and eigenvalues in linear algebra.

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.

Explores the properties and examples of diagonalizable matrices, emphasizing the relationship between eigenvectors and eigenvalues.

Covers the theory and examples of diagonalizing matrices, focusing on eigenvalues, eigenvectors, and linear independence.

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