Singular Values, Fundamental Theorem

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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.