Lectures related to Projection Orthogonal: Importance of Orthogonal Bases

Introduces orthogonal families, orthonormal bases, and projections in linear algebra.

Orthogonal Matrices: Properties and Applications

Explores the properties and applications of orthogonal matrices in linear algebra, focusing on orthogonality and projections.

Coordinate Systems and Applications

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

Orthogonal Bases and Projection

Introduces orthogonal bases, projection onto subspaces, and the Gram-Schmidt process in linear algebra.

Linear Algebra: Lecture Notes

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

Linear Mapping Basics

Covers the basics of linear mapping and coordinate systems.

Linear Independence and Bases

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

Orthogonality and Projection

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

Change of Basis, General Case

Explores the relationship between matrices under different bases in linear algebra.

Gram-Schmidt Algorithm

Covers the Gram-Schmidt algorithm for orthonormal bases in vector spaces.

Orthogonal Families and Projections

Explains orthogonal families, bases, and projections in vector spaces.

Projection in Vector Spaces

Explores the generalization of projection in vector spaces and its unique properties, emphasizing its role in finding the closest vector in a subspace.

Linear Algebra: Matrices and Vector Spaces

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

Orthogonal Bases in Vector Spaces

Covers orthogonal bases, Gram-Schmidt method, linear independence, and orthonormal matrices in vector spaces.

Geometric Transformations in R2 and R3

Explores geometric transformations in R2 and R3, including linear transformations, projections, matrices, and trace properties.

Linear Transformations: Matrices and Bases

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

Orthogonal Complement and Projection

Covers the concept of orthogonal complement and projection in vector spaces.

Linear Transformations: Matrices and Bases

Covers the method to calculate the images of vectors in a given base.

Linear Algebra: Matrix Representation

Explores linear applications in R² and matrix representation, including basis, operations, and geometric interpretation of transformations.

Finding Orthogonal/Orthonormal Base: First Step

Introduces the first step in finding an orthogonal/orthonormal base in a vector space.