Practice Canonical Forms (brief Introduction) (31.5)

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6 sample questions

Question 1.
What is Jordan Canonical Form?
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Think about how matrices can be rearranged for simplicity.
Question 2.
What constitutes a Jordan Block?
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Consider the structure you see in those blocks.
3Question 3.
What does JCF stand for?
- Jordan Canonical Form
- Joint Coordinate Frame
- Just Canonical Form
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Think about the key terms in matrix theory.
4Question 4.
True or False: Every matrix can be diagonalized.
- True
- False
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Recall the properties of eigenvalues.
Question 5.
Given the matrix A = [[6, 1], [0, 6]], find its Jordan Canonical Form.
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Look for the structure with repeated eigenvalues.
Question 6.
Construct the JCF for a matrix that has a 3x3 block with an eigenvalue of 5 and two independent eigenvalues of 2.
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Identify how to organize duplicate eigenvalues into blocks.

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