# 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.

from Singular Value Decomposition - Wikipedia

This topic includes the following resources and journeys:

Filters
28 items

## Singular Value Decomposition (SVD): Overview

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...

See More

## Randomized Singular Value Decomposition (SVD)

13 min
Intermediate
Video
Theory

This video describes how to use recent techniques in randomized linear algebra to efficiently compute the singular value decomposition (SVD) for extremely large matrices.

See More

## SVD: Eigenfaces 3 [Matlab]

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

## Singular Value Decomposition (SVD): Mathematical Overview

12 min
Intermediate
Video
Theory

This video presents a mathematical overview of the singular value decomposition (SVD).

See More

## SVD: Importance of Alignment [Matlab]

6 min
Beginner
Video
Application

This video describes the importance of aligning data when using the singular value decomposition (SVD) (Matlab code).

See More

## SVD Method of Snapshots

4 min
Beginner
Video
Theory

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

See More

## Unitary Transformations and the SVD [Python]

6 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) is related to unitary transformations, with Python code.

See More

## SVD: Eigenfaces 2 [Python]

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

## Singular Value Decomposition (SVD): Dominant Correlations

11 min
Intermediate
Video
Theory

This lectures discusses how the SVD captures dominant correlations in a matrix of data.

See More

## SVD: Image Compression [Python]

9 min
Beginner
Video
Application

This video describes how to use the singular value decomposition (SVD) for image compression in Python.

See More

## SVD and Optimal Truncation

11 min
Intermediate
Video
Theory

This video describes how to truncate the singular value decomposition (SVD) for matrix approximation.

See More

## Unitary Transformations and the SVD [Matlab]

11 min
Intermediate
Video
Application

This video describes how the singular value decomposition (SVD) is related to unitary transformations, with Matlab code.

See More

## SVD: Eigenfaces 2 [Matlab]

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

## Randomized SVD: Power Iterations and Oversampling

4 min
Intermediate
Video
Theory

This video discusses the randomized SVD and how to make it more accurate with power iterations (multiple passes through the data matrix) and oversampling.

See More

## SVD: Image Compression [Matlab]

14 min
Beginner
Video
Application

This video describes how to use the singular value decomposition (SVD) for image compression in Matlab.

See More

## SVD and Alignment: A Cautionary Tale

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.

See More

## SVD: Optimal Truncation [Python]

8 min
Intermediate
Video
Application

This video describes how to optimally truncate the singular value decomposition (SVD) for noisy data (Python code).

See More

## SVD: Eigenfaces 1 [Python]

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

## Randomized SVD Code [Python]

10 min
Beginner
Video
Application

This video describes the randomized singular value decomposition (rSVD) (Python code).

See More

## SVD: Eigenfaces 4 [Matlab]

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: Optimal Truncation [Matlab]

12 min
Intermediate
Video
Application

This video describes how to optimally truncate the singular value decomposition (SVD) for noisy data (Matlab code).

See More

## SVD: Eigenfaces 1 [Matlab]

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

## Randomized SVD Code [Matlab]

9 min
Beginner
Video
Application

This video describes the randomized singular value decomposition (rSVD) (Matlab code).

See More

## SVD: Eigenfaces 3 [Python]

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

## Singular Value Decomposition (SVD): Matrix Approximation

14 min
Intermediate
Video
Theory

This video describes how the singular value decomposition (SVD) can be used for matrix approximation.

See More