Linear Maps: Dimension and Bases

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Projection Orthogonal: Importance of Orthogonal Bases

Emphasizes the importance of using orthogonal bases in linear algebra for representing linear transformations.

Linear Algebra: Matrices and Vector Spaces

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

Linear Independence: Definition and Examples

Explores the concept of linear independence in vector spaces through definitions and illustrative examples.

Linear Algebra Fundamentals

Explores linear algebra fundamentals, including key definitions, theorems, and practical applications in mathematics and technology.

Linear Algebra: Matrix Representation

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

Change of Basis: Transition Matrices

Covers change of basis, transition matrices, and matrix similarity.

Coordinate Systems and Applications

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

Linear Applications and Matrices

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

Linear Mapping and Bases

Explores linear mapping, isomorphism, and change of bases in vector spaces.

Smooth Manifolds: Diffeomorphisms

Explores smooth manifolds through diffeomorphisms and embedded submanifolds in a linear space.