Lectures related to Singular Values, Fundamental Theorem

Characteristic Polynomials and Similar Matrices

Explores characteristic polynomials, similarity of matrices, and eigenvalues in linear transformations.

Eigenvalues and Eigenvectors Decomposition

Covers the decomposition of a matrix into its eigenvalues and eigenvectors, the orthogonality of eigenvectors, and the normalization of vectors.

Orthogonality and Gram-Schmidt Process

Explores orthogonality, Gram-Schmidt process, dot products, and solution minimization in systems.

Linear Applications and Eigenvectors

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

Singular Value Decomposition: Applications and Interpretation

Explains the construction of U, verification of results, and interpretation of SVD in matrix decomposition.

Orthogonal Linear Maps

Covers orthogonal linear maps, orthogonal matrices, invertibility, and least squares solutions in Euclidean spaces.

Orthogonal Bases and Projection

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

Orthogonal/Orthonormal Bases and Polynomials

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Singular Value Decomposition: Orthogonal Vectors and Matrix Decomposition

Explains Singular Value Decomposition, focusing on orthogonal vectors and matrix decomposition.

Diagonalization of Matrices and Least Squares

Covers diagonalization of matrices, eigenvectors, linear maps, and least squares method.

Singular Value Decomposition: Fundamentals and Applications

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

Singular Value Decomposition: Example

Explains the step-by-step process of finding the singular value decomposition of a matrix.

Diagonalization of Matrices

Explores the diagonalization of matrices through eigenvalues and eigenvectors, emphasizing the importance of bases and subspaces.

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

Eigenvalues and Eigenvectors in 3D

Explores eigenvalues and eigenvectors in 3D linear algebra, covering characteristic polynomials, stability under transformations, and real roots.

Singular Value Decomposition

Covers the Singular Value Decomposition theorem and its application in decomposing matrices.

Linear Regression: Absence or Presence of Covariates

Explores linear regression with and without covariates, covering models captured by independent distributions and tools like subspaces and orthogonal projections.

Orthogonal Families and Projections

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

Eigenvalues and Eigenvectors: Understanding Matrix Properties

Explores eigenvalues and eigenvectors, demonstrating their importance in linear algebra and their application in solving systems of equations.

Orthogonality and Projection

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