Linear Algebra: Orthogonal Projection and QR Factorization

Related lectures (28)

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Explains the method of least squares in linear regression to find the best-fitting line to a set of data points.

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

Explores matrix equivalence theorems for systems of equations and least squares solutions.

Explains how to solve linear equations using the least squares method to minimize errors in the system.

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

Explores orthogonal projection in Euclidean space, emphasizing uniqueness and calculation methods.

Explores orthogonal projections and the Gram-Schmidt method for constructing bases.

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

Explains the QR factorization theorem and demonstrates the Gram-Schmidt procedure with an example.

Delves into singular value decomposition and its applications in linear algebra.