Lectures related to Orthogonal transformation

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

Covers scalar products, orthogonal vectors, norms, and projections in vector spaces, emphasizing orthonormal families of vectors.

Matrices and Orthogonal Transformations

Explores orthogonal matrices and transformations, emphasizing preservation of norms and angles.

Singular Value Decomposition: Fundamentals and Applications

Explores the fundamentals of Singular Value Decomposition, including orthonormal bases and practical applications.

Orthogonal Projection: Uniqueness and Properties

Explores the uniqueness and properties of orthogonal projection, including decomposition, associated matrix, linearity, and practical examples.

Projections and Symmetries

Explores projections on lines and symmetries in 2D space, emphasizing fixed points and symmetric matrices.

QR Factorization: Orthogonal Bases and Matrices

Explores QR factorization, orthogonal bases, and matrices for numerical computations and solving systems of equations.

Orthogonal Matrices & Spectral Decomposition

Covers the process of finding orthogonal bases and spectral decomposition of symmetric matrices.

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

Best approximative subspace

Explores finding the minimal solution of a problem using orthogonal bases and factorization, emphasizing uniqueness and practical examples.

Orthogonal Projections in Linear Algebra

Explores orthogonal projections, orthonormal bases, and QR factorization in linear algebra.

Singular Values, Fundamental Theorem

Explores the fundamental theorem on singular values and the formation of orthonormal bases from eigenvectors.

Gram-Schmidt Process and QR Decomposition

Covers the Gram-Schmidt process, QR decomposition, orthogonal projection theorem, and matrix formulas.

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.

Isometries in R^n

Explores the standard form of isometries in R^n and the preservation of distances.

Orthogonal Bases in Vector Spaces

Explores orthogonal bases in vector spaces, explaining unique vector representations and spectral decomposition.

Orthogonal Bases in Vector Spaces

Covers the concept of orthogonal bases in vector spaces and Pythagorean theorem applications.

Signal Approximation and Orthogonal Bases

Explores signal approximation, orthogonal bases, Fourier series, correlation, and vector geometry.

Orthogonal Complement and Projection

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

Finding Orthogonal/Orthonormal Base: First Step

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