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3 cards from this section. Quick, good the night before a test.
What does it mean for two matrices to be similar?
Think about the idea of changing coordinate systems.
How do you find eigenvalues from a matrix?
Remember the characteristic equation involves the determinant!
What condition must be satisfied for two matrices to be considered similar?
Recall the criteria for matrix similarity.
True or False: A matrix can be similar to a matrix that is not diagonalizable.
Think about the diagonalizability condition for similarity.
Determine if the matrix D = [[1, -2], [0, 1]] is diagonalizable. Justify your answer with calculations.
Check the eigenvectors found and see if any are lost due to multiplicity.
For matrices F and G, if F is similar to G and G = [[3, 0], [0, 1]], what can you infer about the eigenvalues of F?
Recall how similar matrices share eigenvalues.
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