Singular Value Decomposition Online Test

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Singular Value Decomposition

Description: This quiz will test your understanding of Singular Value Decomposition (SVD), a technique for factorizing matrices into a product of three matrices.
Number of Questions: 15
Created by: Aliensbrain Bot
Tags: linear algebra matrix factorization singular value decomposition

What is the general form of the Singular Value Decomposition (SVD) of a matrix?

A = UΣV^T
A = UΣV
A = UΣ^T V^T
A = UΣ^T V

What are the singular values of a matrix?

The eigenvalues of the matrix
The square roots of the eigenvalues of the matrix
The diagonal entries of the matrix
The non-zero entries of the matrix

What is the relationship between the singular values and the rank of a matrix?

The rank of a matrix is equal to the number of non-zero singular values
The rank of a matrix is equal to the number of singular values
The rank of a matrix is equal to the sum of the singular values
The rank of a matrix is equal to the product of the singular values

What is the geometric interpretation of the singular value decomposition?

It rotates and scales the matrix to make it diagonal
It projects the matrix onto a subspace
It decomposes the matrix into a sum of rank-one matrices
It finds the eigenvectors and eigenvalues of the matrix

What are some applications of the singular value decomposition?

Image compression
Principal component analysis
Linear regression
All of the above

What is the computational complexity of the singular value decomposition?

O(n^3)
O(n^2)
O(n log n)
O(n)

What is the relationship between the SVD and the QR decomposition?

The SVD is a generalization of the QR decomposition
The QR decomposition is a generalization of the SVD
The SVD and the QR decomposition are unrelated
The SVD and the QR decomposition are equivalent

What is the relationship between the SVD and the eigenvalue decomposition?

The SVD is a generalization of the eigenvalue decomposition
The eigenvalue decomposition is a generalization of the SVD
The SVD and the eigenvalue decomposition are unrelated
The SVD and the eigenvalue decomposition are equivalent

What is the relationship between the SVD and the polar decomposition?

The SVD is a generalization of the polar decomposition
The polar decomposition is a generalization of the SVD
The SVD and the polar decomposition are unrelated
The SVD and the polar decomposition are equivalent

What is the relationship between the SVD and the LU decomposition?

The SVD is a generalization of the LU decomposition
The LU decomposition is a generalization of the SVD
The SVD and the LU decomposition are unrelated
The SVD and the LU decomposition are equivalent

What is the relationship between the SVD and the Cholesky decomposition?

The SVD is a generalization of the Cholesky decomposition
The Cholesky decomposition is a generalization of the SVD
The SVD and the Cholesky decomposition are unrelated
The SVD and the Cholesky decomposition are equivalent

What is the relationship between the SVD and the QR decomposition with column pivoting?

The SVD is a generalization of the QR decomposition with column pivoting
The QR decomposition with column pivoting is a generalization of the SVD
The SVD and the QR decomposition with column pivoting are unrelated
The SVD and the QR decomposition with column pivoting are equivalent

What is the relationship between the SVD and the eigenvalue decomposition with scaling?

The SVD is a generalization of the eigenvalue decomposition with scaling
The eigenvalue decomposition with scaling is a generalization of the SVD
The SVD and the eigenvalue decomposition with scaling are unrelated
The SVD and the eigenvalue decomposition with scaling are equivalent

What is the relationship between the SVD and the polar decomposition with scaling?

The SVD is a generalization of the polar decomposition with scaling
The polar decomposition with scaling is a generalization of the SVD
The SVD and the polar decomposition with scaling are unrelated
The SVD and the polar decomposition with scaling are equivalent

What is the relationship between the SVD and the LU decomposition with scaling?

The SVD is a generalization of the LU decomposition with scaling
The LU decomposition with scaling is a generalization of the SVD
The SVD and the LU decomposition with scaling are unrelated
The SVD and the LU decomposition with scaling are equivalent

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