Generalized Eigenvectors and Jordan Form
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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.
For the only eigenvalue is . Find the geometric multiplicity .
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About these 110 questions
Minimal polynomials, the Cayley-Hamilton theorem, generalized eigenvectors, Jordan normal form, and the matrix exponential. This set covers the chapter Generalized Eigenvectors and Jordan Form in Linear Algebra: 37 easy, 44 medium and 29 hard questions, each graded instantly with a hint and a full step-by-step solution. Progress is saved in this browser only.
- Why diagonalization fails — 13 questions
- Invariant subspaces — 8 questions
- The Cayley–Hamilton theorem — 11 questions
- The minimal polynomial — 12 questions
- Generalized eigenvectors — 10 questions
- Nilpotent operators and Jordan chains — 11 questions
- Jordan blocks and the normal form — 15 questions
- Building a Jordan basis — 9 questions
- Powers and functions of a matrix — 10 questions
- The matrix exponential and linear systems — 11 questions
For work on paper there is a printable problem set with separate worked solutions.