11. Eigenvalues and Eigenvectors

Diagonalization Criteria — Quiz

Test your understanding of diagonalization criteria with 5 practice questions.

Practice Questions

Question 1

Which condition guarantees that an $n\times n$ matrix is diagonalizable?

Question 2

If an $n\times n$ matrix has $n$ distinct eigenvalues, what can you conclude?

Question 3

A $3\times3$ matrix has three linearly independent eigenvectors. What is true?

Question 4

A $2\times2$ matrix has only one linearly independent eigenvector. What can you conclude?

Question 5

If $A=PDP^{-1}$, what does the diagonal matrix $D$ contain?