Orthogonal Projections in Linear Algebra

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Related lectures (24)

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Orthogonality and Projection

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

Orthogonal Bases and Projection

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

Orthogonal Projection Theorems

Covers the theorems related to orthogonal projection and orthonormal bases.

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.

Orthogonal Projection in Linear Algebra

Explains orthogonal projection in linear algebra, focusing on transforming non-orthogonal bases into orthogonal ones.

Orthogonal Projection: Uniqueness and Properties

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

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.

Singular Value Decomposition: Applications and Interpretation

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