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.
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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 is the characteristic polynomial of this matrix?
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?
needs only the powers and
from “Matrix Powers by Diagonalization”
D = (2 0; 0 4). What is ?
(4 0; 0 16)
from “Matrix Powers by Diagonalization”