Lecture

Singular Value Decomposition

Description

This lecture covers the singular value decomposition theorem for a matrix A of rank r, where Σ is a diagonal matrix with non-zero singular values of A, and U, V are orthogonal matrices such that A = UV. The lecture explains the proof by constructing orthonormal bases, normalizing them, and completing them to form an orthonormal basis. The process involves transforming bases, normalizing vectors, and decomposing A into UΣV. The lecture concludes with the matrix representation of the decomposition.

In MOOCs (9)

Instructor

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Official source

https://mediaspace.epfl.ch/media/0_91r143jg

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Ontological neighbourhood

Mathematics

Algebra: Linear algebra

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