Lectures related to Vector Spaces: Operations and Linear Transformations

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

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

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

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

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

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

Introduces abstract concepts in linear algebra, focusing on operations with vectors and matrices.

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

Covers matrix kernels, images, linear applications, independence, and bases in vector spaces.

Covers the definition and properties of vector spaces, along with examples like Euclidean spaces and matrix spaces.

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

Explores the properties of linear transformations through step-by-step calculations and matrix manipulations.

Introduces vector spaces, subspaces, linear maps, and evaluation maps, with examples and exercises for better comprehension.

Introduces linear combinations in vector spaces, operations, and polynomials of degree 2.

Explores vector space properties, operations, linear combinations, and subspaces construction.

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

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

Introduces linear combinations of vectors in R^n and their properties.

Covers the definition and examples of vector spaces, including subspaces and linear transformations.

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