12. Diagonalization and Dynamical Systems

Simplifying Repeated Matrix Computation — Quiz

Test your understanding of simplifying repeated matrix computation with 5 practice questions.

Practice Questions

Question 1

If a matrix satisfies $A = P D P^{-1}$, what is the most efficient formula for $A^n$?

Question 2

If $D = \begin{pmatrix}2 & 0 \\ 0 & 3\end{pmatrix}$, what is $D^4$?

Question 3

For the recurrence $x_{k+1} = A x_k$, what is $x_n$ in terms of $x_0$?

Question 4

Why does diagonalization simplify repeated matrix computation?

Question 5

If $A$ is diagonalizable and has eigenvalues $2$ and $-1$, what are the eigenvalues of $A^3$?