Lectures related to Linear Algebra: Spanning and Combining Vectors

Matrix Operations: Linear Systems and Solutions

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

Dirac's Notation, Tensor Product

Covers Dirac's notation in linear algebra and the tensor product concept in Hilbert spaces.

Linear Algebra: Matrices and Vector Spaces

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

Linear Algebra in Dirac Notation

Covers linear algebra in Dirac notation, focusing on vector spaces and quantum bits.

Vector Spaces: Properties and Operations

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

Linear Algebra Basics

Covers the basics of linear algebra, emphasizing the identification of subspaces through key properties.

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 Combinations: Vectors and Matrices

Explores linear combinations of vectors and matrices in Rn, demonstrating geometric interpretations and matrix operations.

Linear Algebra: Vector Spaces and Linear Independence

Covers vector spaces, operations, and linear independence with examples from polynomials and functions.

Scalar Product and Vectors

Introduces vector components, scalar and vector products, and their properties, including colinear and coplanar vectors, and the rule of the right hand.

Linear Independence and Bases

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

Vector Calculus in 3D

Covers the concept of 3D vector space, scalar product, bases, orthogonality, and projections.

Linear Algebra: Linear Dependence and Independence

Explores linear dependence and independence of vectors in geometric spaces.

Linear Algebra: Vector Spaces

Explores vector spaces, subspaces, bases, and linear combinations in R² and R³, including free and linked families.

Orthogonality and Projection

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

Vector Equations and Linear Combinations

Covers vector equations, linear combinations, and the span of vectors.

Linear Applications and Eigenvectors

Covers linear applications, diagonalizable matrices, eigenvectors, and orthogonal subspaces in R^n.

Linear Algebra in R³: Vector Spaces

Explores vector spaces in three dimensions, covering linear combinations, subspaces, and properties of families of vectors in R³.

Linear Algebra: Properties and Equations

Introduces algebraic properties, vector equations, and matrix operations.

Vector Spaces and Linear Applications

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