Linear Maps and Linear Independence

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Related lectures (24)

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Linear Algebra: Bases and Dimension

Explores linear independence, bases, and dimension in vector spaces with examples involving matrices and polynomials.

Generalization of Change of Basis Matrices

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

Linear Independence in Vector Spaces

Explores linear independence in vector spaces and the concept of bases.

Linear Independence and Basis

Explains linear independence, basis, and matrix rank with examples and exercises.

Vector Spaces and Linear Applications

Covers vector spaces, subspaces, kernel, image, linear independence, and bases in linear algebra.

Linear Maps and Matrices

Covers linear maps, matrices, and applications, including exercises on bases and invertibility.

Linear Algebra: Lecture Notes

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

Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Coordinate Systems and Applications

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

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.