Lectures related to Linear Maps and Linear Independence

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

Linear Algebra: Matrices and Vector Spaces

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

Linear Independence and Bases in Vector Spaces

Explains linear independence, bases, and dimension in vector spaces, including the importance of the order of vectors in a basis.

Linear Independence and Bases

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

Linear Transformations: Polynomials and Bases

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

Vector Spaces Equivalence

Explores equivalence in vector spaces, covering conditions for statements to be considered equivalent and properties of algebraic bases.

Linear Algebra Basics

Covers the basics of linear algebra, including linear maps, bases, and matrix operations.

Vector Spaces: Bases and Dimension

Explores bases, dimensions, and matrix ranks in vector spaces with practical examples and proofs.

Linear Independence: Definition and Examples

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

Orthogonality and Projection

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

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.