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Singular Value Decomposition

This quiz will test your understanding of Singular Value Decomposition (SVD), a technique for factorizing matrices into a product of three matrices.

15 Questions Published
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Questions

Question 1 Multiple Choice (Single Answer)

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

  1. A = UΣV^T
  2. A = UΣV
  3. A = UΣ^T V^T
  4. A = UΣ^T V
Question 2 Multiple Choice (Single Answer)

What are the singular values of a matrix?

  1. The eigenvalues of the matrix
  2. The square roots of the eigenvalues of the matrix
  3. The diagonal entries of the matrix
  4. The non-zero entries of the matrix
Question 3 Multiple Choice (Single Answer)

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

  1. The rank of a matrix is equal to the number of non-zero singular values
  2. The rank of a matrix is equal to the number of singular values
  3. The rank of a matrix is equal to the sum of the singular values
  4. The rank of a matrix is equal to the product of the singular values
Question 4 Multiple Choice (Single Answer)

What is the geometric interpretation of the singular value decomposition?

  1. It rotates and scales the matrix to make it diagonal
  2. It projects the matrix onto a subspace
  3. It decomposes the matrix into a sum of rank-one matrices
  4. It finds the eigenvectors and eigenvalues of the matrix
Question 5 Multiple Choice (Single Answer)

What are some applications of the singular value decomposition?

  1. Image compression
  2. Principal component analysis
  3. Linear regression
  4. All of the above
Question 6 Multiple Choice (Single Answer)

What is the computational complexity of the singular value decomposition?

  1. O(n^3)
  2. O(n^2)
  3. O(n log n)
  4. O(n)
Question 7 Multiple Choice (Single Answer)

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

  1. The SVD is a generalization of the QR decomposition
  2. The QR decomposition is a generalization of the SVD
  3. The SVD and the QR decomposition are unrelated
  4. The SVD and the QR decomposition are equivalent
Question 8 Multiple Choice (Single Answer)

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

  1. The SVD is a generalization of the eigenvalue decomposition
  2. The eigenvalue decomposition is a generalization of the SVD
  3. The SVD and the eigenvalue decomposition are unrelated
  4. The SVD and the eigenvalue decomposition are equivalent
Question 9 Multiple Choice (Single Answer)

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

  1. The SVD is a generalization of the polar decomposition
  2. The polar decomposition is a generalization of the SVD
  3. The SVD and the polar decomposition are unrelated
  4. The SVD and the polar decomposition are equivalent
Question 10 Multiple Choice (Single Answer)

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

  1. The SVD is a generalization of the LU decomposition
  2. The LU decomposition is a generalization of the SVD
  3. The SVD and the LU decomposition are unrelated
  4. The SVD and the LU decomposition are equivalent
Question 11 Multiple Choice (Single Answer)

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

  1. The SVD is a generalization of the Cholesky decomposition
  2. The Cholesky decomposition is a generalization of the SVD
  3. The SVD and the Cholesky decomposition are unrelated
  4. The SVD and the Cholesky decomposition are equivalent
Question 12 Multiple Choice (Single Answer)

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

  1. The SVD is a generalization of the QR decomposition with column pivoting
  2. The QR decomposition with column pivoting is a generalization of the SVD
  3. The SVD and the QR decomposition with column pivoting are unrelated
  4. The SVD and the QR decomposition with column pivoting are equivalent
Question 13 Multiple Choice (Single Answer)

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

  1. The SVD is a generalization of the eigenvalue decomposition with scaling
  2. The eigenvalue decomposition with scaling is a generalization of the SVD
  3. The SVD and the eigenvalue decomposition with scaling are unrelated
  4. The SVD and the eigenvalue decomposition with scaling are equivalent
Question 14 Multiple Choice (Single Answer)

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

  1. The SVD is a generalization of the polar decomposition with scaling
  2. The polar decomposition with scaling is a generalization of the SVD
  3. The SVD and the polar decomposition with scaling are unrelated
  4. The SVD and the polar decomposition with scaling are equivalent
Question 15 Multiple Choice (Single Answer)

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

  1. The SVD is a generalization of the LU decomposition with scaling
  2. The LU decomposition with scaling is a generalization of the SVD
  3. The SVD and the LU decomposition with scaling are unrelated
  4. The SVD and the LU decomposition with scaling are equivalent
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