21.13 - Minimal Polynomial
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Practice Questions
Test your understanding with targeted questions
Define minimal polynomial in your own words.
💡 Hint: Think about what it means for a polynomial to 'annihilate' a matrix.
What is a monic polynomial?
💡 Hint: What do you recall about polynomial coefficients?
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the minimal polynomial of a matrix?
💡 Hint: Focus on the purpose of the polynomial.
True or False: The minimal polynomial of a matrix can never be of higher degree than the characteristic polynomial.
💡 Hint: Think about the degree relationship between the two polynomials.
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Challenge Problems
Push your limits with advanced challenges
Find the minimal polynomial for the matrix A = [[3, 1, 0], [0, 3, 1], [0, 0, 3]]. What does this tell you about A?
💡 Hint: Calculate the characteristic polynomial first.
Evaluate the implications of a minimal polynomial m(x) = x^3 for a 3x3 matrix. What structure does this imply for the eigenvalues?
💡 Hint: Consider the multiplicity of the eigenvalues.
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