21.13.1 - Definition
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Practice Questions
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What is the minimal polynomial of a matrix?
💡 Hint: Think about polynomials and matrices.
Does the minimal polynomial divide the characteristic polynomial?
💡 Hint: Consider how these polynomials relate to eigenvalues.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the degree of the minimal polynomial related to?
💡 Hint: Think about how polynomials relate in linear algebra.
Is it true that the minimal polynomial must be a factor of the characteristic polynomial?
💡 Hint: Recall their mathematical relationship.
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Challenge Problems
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Given the matrix A = [[1, 2],[0, 1]], find its minimal polynomial and explain your reasoning.
💡 Hint: Calculate the eigenvalues and their multiplicities.
If a matrix has a minimal polynomial of m(x) = (x - 3)(x - 2)^2, what can you infer about its eigenvalues and their respective multiplicities?
💡 Hint: Review the factors and their powers.
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