Vector Spaces: Dimension and Generators

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Related lectures (27)

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Linear Independence and Bases

Covers linear independence, bases, and coordinate systems with examples and theorems.

Orthogonality and Characters

Explains orthogonality and characters in group representations, including equivalence classes and vector space dimensions.

Vector Spaces: Definitions and Properties

Covers the definitions and properties of vector spaces, including axioms and examples.

Generalization of Change of Basis Matrices

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

Polynomials: Operations and Properties

Explores polynomial operations, properties, and subspaces in vector spaces.

Vector Spaces: Definitions and Properties

Covers the definition of vector spaces, subspaces, and linear combinations of vectors.

Linear Operators: Boundedness and Spaces

Explores linear operators, boundedness, and vector spaces with a focus on verifying bounded aspects.

Linear Transformations: Matrices and Bases

Covers the determination of matrices associated with linear transformations and explores the kernel and image concepts.

Linear Algebra: Lecture Notes

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

Linear Applications: Definitions and Properties

Explores the definition and properties of linear applications, focusing on injectivity, surjectivity, kernel, and image, with a specific emphasis on matrices.