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3 cards from this section. Quick, good the night before a test.
What is an eigenvalue?
Think about how a matrix can transform a vector.
Define an eigenvector.
Look for vectors that keep their direction after transformation.
What is the characteristic equation used to find eigenvalues?
Think about how we determine if a matrix is singular.
True or False: An eigenvector can be the zero vector.
Remember the definition of an eigenvector.
Given the matrix C = [[3, 0], [0, 4]], find the eigenvalues and describe their significance for a physical system.
Use the characteristic polynomial to determine the eigenvalues.
Consider a dynamics problem in civil engineering where a building's stiffness matrix K has eigenvalues of 2 and 5. How would these eigenvalues affect the building's response?
Think about the implications of natural frequencies in structural dynamics.
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