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3 cards from this section. Quick, good the night before a test.
What is the definition of a minimal polynomial?
Think about the polynomial's role concerning the matrix.
True or False: The minimal polynomial must always be of higher degree than the characteristic polynomial.
Consider their relationship.
What defines a minimal polynomial?
Think about the polynomial's role in matrix equations.
True or False: The minimal polynomial only applies to square matrices.
Recall the definition of a minimal polynomial.
You encounter a 3x3 matrix with a characteristic polynomial of (λ-1)(λ-2)². Determine the minimal polynomial and discuss its implications on stability.
Reflect on the meaning of repeated roots in the context of Jordan forms.
Consider a matrix with eigenvalues 3, 4, and a repeated eigenvalue of 5. How would this affect its minimal polynomial and theorize on the potential behavior of the system modeled by this matrix?
Think about how multiple eigenvalues affect system dynamics, particularly in control systems.
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