12. Diagonalization and Dynamical Systems

Interpreting Dominant Eigenvalues — Quiz

Test your understanding of interpreting dominant eigenvalues with 5 practice questions.

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Practice Questions

Question 1

In a diagonalizable dynamical system, what is the dominant eigenvalue?

Question 2

If a matrix has eigenvalues $6$, $2$, and $-1$, which eigenvalue is dominant?

Question 3

If the dominant eigenvalue of a dynamical system has absolute value less than $1$, what happens to repeated iterates as $n$ increases?

Question 4

A system has dominant eigenvalue $-4$ and all other eigenvalues have smaller absolute value. What is the main long-term effect of the dominant eigenvalue on repeated multiplication?

Question 5

Which eigenvalue is dominant among $5$, $-3$, and $4$?