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3 cards from this section. Quick, good the night before a test.
Define what an eigenvector is.
Think about what happens to a vector when multiplied by a matrix.
What does the characteristic equation help you find?
Recall the determinant condition.
What must be true for a matrix to have a non-trivial solution for its eigenvectors?
Refer to the conditions for finding eigenvalues.
Solving the equation Ax = λx leads to what condition for eigenvalues?
Think about the transformations involved.
Consider the matrix C = [[2, -1], [1, 0]]. Find its eigenvalues and eigenvectors and interpret their significance in a physical system.
Start with the determinant to find eigenvalues, then solve for eigenvectors.
Given a linear transformation matrix D that represents a vibrating system, find the eigenvalues and discuss how they can predict the system's behavior under oscillations.
Relate your result back to the physical interpretation in terms of energy states.
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