Linear Algebra: Lecture Notes

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Related lectures (25)

Page 2 of 3

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Linear Applications and Span

Introduces linear applications, span, kernels, and images in vector spaces with illustrative examples and theorems.

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 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.

Orthogonality and Projection

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

Linear Algebra: Matrix Operations and Basis

Explores matrix operations, rank determination, kernel dimensions, and basis concepts in linear algebra.

Matrix Operations: Linear Systems and Solutions

Explores matrix operations, linear systems, solutions, and the span of vectors in linear algebra.

Vector Spaces: Definitions and Examples

Covers the definition and examples of vector spaces, including subspaces and linear transformations.

Vector Spaces: Bases and Dimension

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

Vector Spaces and Linear Applications

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