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Singular Value Decomposition (SVD)

In linear algebra, the singular value decomposition (SVD) is a factorization of a real or complex matrix that generalizes the eigendecomposition of a square normal matrix to any m × n matrix via an extension of the polar decomposition.

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Singular Value Decomposition (SVD): Overview
1

Singular Value Decomposition (SVD): Overview

Steve Brunton
6 min
Beginner
Video
Theory

This video presents an overview of the singular value decomposition (SVD), which is one of the most widely used algorithms for data processing, reduced-order modeling, and high-dimensional...

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SVD: Eigenfaces 1 [Matlab]
0

SVD: Eigenfaces 1 [Matlab]

Steve Brunton
7 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used to efficiently represent human faces, in the so-called "eigenfaces" (Matlab code, part 1).

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SVD: Eigenfaces 3 [Python]
0

SVD: Eigenfaces 3 [Python]

Steve Brunton
5 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used to efficiently represent human faces, in the so-called "eigenfaces" (Python code, part 3).

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SVD: Eigen Action Heros [Matlab]
0

SVD: Eigen Action Heros [Matlab]

Steve Brunton
16 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used to efficiently represent human faces. In this example, we represent action heros (Matlab).

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Least Squares Regression and the SVD
0

Least Squares Regression and the SVD

Steve Brunton
5 min
Beginner
Video
Theory

This video describes how the SVD can be used to solve linear systems of equations. In particular, it is possible to solve nonsquare systems (overdetermined or underdetermined) via least...

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SVD: Eigenfaces 3 [Matlab]
0

SVD: Eigenfaces 3 [Matlab]

Steve Brunton
10 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used to efficiently represent human faces, in the so-called "eigenfaces" (Matlab code, part 3).

See More
SVD Method of Snapshots
0

SVD Method of Snapshots

Steve Brunton
4 min
Beginner
Video
Theory

This video describes how to compute the singular value decomposition (SVD) using the method of snapshots, by Sirovich 1987.

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SVD: Eigenfaces 2 [Python]
0

SVD: Eigenfaces 2 [Python]

Steve Brunton
10 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used to efficiently represent human faces, in the so-called "eigenfaces" (Python code, part 2).

See More
SVD: Eigenfaces 2 [Matlab]
0

SVD: Eigenfaces 2 [Matlab]

Steve Brunton
8 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used to efficiently represent human faces, in the so-called "eigenfaces" (Matlab code, part 2).

See More
SVD and Alignment: A Cautionary Tale
0

SVD and Alignment: A Cautionary Tale

Steve Brunton
7 min
Intermediate
Video
Theory

This video describes the importance of data alignment when performing the singular value decomposition (SVD). Translations and rotations both present challenges for the SVD.

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SVD: Eigenfaces 1 [Python]
0

SVD: Eigenfaces 1 [Python]

Steve Brunton
4 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) can be used to efficiently represent human faces, in the so-called "eigenfaces" (Python code, part 1).

See More
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