31.5 - Canonical Forms (Brief Introduction)
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Practice Questions
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What is Jordan Canonical Form?
💡 Hint: Think about how matrices can be rearranged for simplicity.
What constitutes a Jordan Block?
💡 Hint: Consider the structure you see in those blocks.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does JCF stand for?
💡 Hint: Think about the key terms in matrix theory.
True or False: Every matrix can be diagonalized.
💡 Hint: Recall the properties of eigenvalues.
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Challenge Problems
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Given the matrix A = [[6, 1], [0, 6]], find its Jordan Canonical Form.
💡 Hint: Look for the structure with repeated eigenvalues.
Construct the JCF for a matrix that has a 3x3 block with an eigenvalue of 5 and two independent eigenvalues of 2.
💡 Hint: Identify how to organize duplicate eigenvalues into blocks.
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