32.14 - Summary Table of Concepts
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is an eigenvector?
💡 Hint: Remember that `λ` is the eigenvalue.
Define eigenspace.
💡 Hint: Think about the vectors that satisfy `Av = λv`.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What defines an eigenvector?
💡 Hint: Focus on the eigenvalue equation.
True or False: The eigenvalue's algebraic multiplicity can be greater than its geometric multiplicity.
💡 Hint: Remember the definitions of both types of multiplicity.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given a matrix A = [[2, 1], [1, 2]], find its eigenvalues and eigenvectors. Discuss if it is diagonalizable.
💡 Hint: Remember to use the determinant for the characteristic polynomial.
Consider a symmetric matrix B with eigenvalues 4, 4, and 2. Determine the geometric and algebraic multiplicities, and explain the implications for diagonalization.
💡 Hint: Think about how the multiplicities relate to the eigenspace dimensions.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.