Coordinate Application: Components and Bases

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

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Covers linear transformations between polynomial spaces and explores examples of linear independence and bases.

Linear Algebra: Lecture Notes

Covers determining vector spaces, calculating kernels and images, defining bases, and discussing subspaces and vector spaces.

Linear Algebra: Subspaces and Transformations

Explores subspaces in linear algebra and transformations, including kernels and images of linear transformations.

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Kernel, Image and Linear Maps

Explains kernel, image, and linear maps, illustrating concepts with examples.

Vector Spaces: Properties and Operations

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

Basis Extraction and Coordinate Application in Vector Spaces

Covers the extraction of bases from families of vectors and the concept of coordinate application in vector spaces.

Projection Orthogonal: Importance of Orthogonal Bases

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

Generalization of Change of Basis Matrices

Covers linear algebra basics, including matrices, change of basis, and invertible matrices.