Lectures related to Orthogonal matrix

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.

Linear Applications and Eigenvectors

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

Symmetric Matrices: Properties and Decomposition

Covers examples of symmetric matrices and their properties, including eigenvectors and eigenvalues.

Orthogonal Families and Projections

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

Orthogonal Projection on Vector Subspace

Explains orthogonal projection on a vector subspace in Euclidean space.

QR Factorization: Orthogonal Bases and Matrices

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

Isometries in R^n

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

Orthogonal Matrices & Spectral Decomposition

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

Gram-Schmidt Process: Orthogonal Vectors

Explores the Gram-Schmidt process for constructing orthogonal vectors in a vector space.

Matrices and Orthogonal Transformations

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

Spectral Theorem Recap

Revisits the spectral theorem for symmetric matrices, emphasizing orthogonally diagonalizable properties and its equivalence with symmetric bilinear forms.

Orthogonal Projections and Best Approximation

Explains orthogonal matrices, Gram-Schmidt process, and best vector approximation in subspaces.

Signal Representations

Covers signal representations using scaling functions and orthonormal properties.

Matrix Operations and Orthogonality

Covers matrix operations, scalar product, orthogonality, and bases in vector spaces.

Elementary Matrices

Covers elementary matrices and their operations in matrix algebra, highlighting their importance in linear algebra.

Physics 1: Vectors and Dot Product

Covers the properties of vectors, including commutativity, distributivity, and linearity.

SVD: Singular Value Decomposition

Covers the concept of Singular Value Decomposition (SVD) for compressing information in matrices and images.

Decomposition Spectral: Symmetric Matrices

Covers the decomposition of symmetric matrices into eigenvalues and eigenvectors.

Multivariate Statistics: Wishart and Hotelling T²

Explores the Wishart distribution, properties of Wishart matrices, and the Hotelling T² distribution, including the two-sample Hotelling T² statistic.