Eigenvalues and Eigenvectors flashcards
10 practice cards drawn from the Eigenvalues and Eigenvectors lessons. Tap a card to turn it over. Every answer is checked against the lesson it came from.
Read the Eigenvalues and Eigenvectors lessons in full →
A (2; 1) = 6 (2; 1). What is A (4; 2)?
(24; 12)
from “Eigenvalues and Eigenvectors”
A (1; 1) = 4 (1; 1). What is A (3; 3)?
(12; 12)
from “Eigenvalues and Eigenvectors”
What does look like?
comes off the main diagonal only
from “The Characteristic Polynomial”
What are the eigenvalues of this matrix?
6 and 1
from “The Characteristic Polynomial”
One eigenvalue of A is -1. Which column is its eigenvector?
(1; −1)
from “Finding an Eigenvector”
Why do both rows of give the same condition?
its determinant is 0, so one row is a multiple of the other
from “Finding an Eigenvector”
What stops a matrix from being diagonalized this way?
it does not have two independent eigenvectors
from “Diagonalizing a 2 × 2 Matrix”
Which equation defines the diagonalization of A?
from “Diagonalizing a 2 × 2 Matrix”
Why is less work through than by multiplying A five times?
a diagonal power is five ordinary powers of numbers
from “Matrix Powers by Diagonalization”
D = (2 0; 0 4). What is ?
(4 0; 0 16)
from “Matrix Powers by Diagonalization”