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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 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).

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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
SVD: Eigenfaces 4 [Matlab]
0

SVD: Eigenfaces 4 [Matlab]

Steve Brunton
6 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 4).

See More
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).

See More
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).

See More
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