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4 cards from this section. Quick, good the night before a test.
What is the condition for a matrix to be diagonalizable?
Consider the relationship between eigenvalues and the independence of eigenvectors.
Define eigenvalue in your own words.
Think about what happens to vectors when transformed by matrices.
What does it mean for a matrix to be diagonalizable?
Think of the properties of the eigenvectors.
True or False: All matrices with repeated eigenvalues are non-diagonalizable.
Consider examples of matrices with distinct eigenvalues.
Given the matrix A = [2 3; 2 4], demonstrate if A is diagonalizable and find its eigenvalues and eigenvectors.
Focus on the linearly independent nature of the eigenvectors.
Prove the Jordan form is useful for non-diagonalizable matrices by providing an example and explaining the process.
Think about the roles of blocks in Jordan form.
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