The Singular Value Decomposition
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Each question is graded on a single answer: a check that this chapter's methods work, not a test of the reasoning behind them.
The singular values of are the square roots of the eigenvalues of . For , find .
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About these 116 questions
Singular values, the SVD, the pseudoinverse, low-rank approximation, and principal component analysis. This set covers the chapter The Singular Value Decomposition in Linear Algebra: 42 easy, 48 medium and 26 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.
- Singular values and the geometry of a matrix — 13 questions
- The singular value decomposition — 16 questions
- The four fundamental subspaces — 10 questions
- Rank, numerical rank, and matrix norms — 12 questions
- The condition number — 11 questions
- Low-rank approximation — 13 questions
- The Moore–Penrose pseudoinverse — 12 questions
- Principal component analysis — 14 questions
- The polar decomposition — 7 questions
- Applications — 8 questions
For work on paper there is a printable problem set with separate worked solutions.