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3 cards from this section. Quick, good the night before a test.
What is the characteristic equation of a 2x2 matrix?
Think of how you find eigenvalues.
Define eigenvalue in your own words.
Consider stretching and direction.
What do we call the equation used to find eigenvalues?
It's the equation that helps in finding eigenvalues.
Eigenvectors are always parallel to the original vectors.
Consider eigenvector definitions.
Given a 3x3 matrix A = [[2, 1, 1], [1, 2, 1], [1, 1, 2]], calculate its eigenvalues and eigenvectors.
Use the characteristic polynomial for step one.
Why is it important for the eigenvector matrices corresponding to distinct eigenvalues to be orthogonal in real symmetric matrices?
Consider how these directions are used in practical applications.
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