11. Eigenvalues and Eigenvectors

Algebraic Vs Geometric Multiplicity — Quiz

Test your understanding of algebraic vs geometric multiplicity with 5 practice questions.

Practice Questions

Question 1

What does algebraic multiplicity of an eigenvalue mean?

Question 2

What does geometric multiplicity of an eigenvalue mean?

Question 3

If the characteristic polynomial is $(\lambda - 2)^3(\lambda + 1)$, what is the algebraic multiplicity of the eigenvalue $2$?

Question 4

If the eigenspace for an eigenvalue has dimension $2$, what is its geometric multiplicity?

Question 5

Which statement is always true for any eigenvalue of a matrix?