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3 cards from this section. Quick, good the night before a test.
Define a diagonal matrix.
Think about the placement of zeroes in a matrix.
What is an eigenvector?
Consider how vectors interact with linear transformations.
What is a diagonal matrix?
Remember where zeroes are placed in such matrices.
True or False: If a matrix has repeated eigenvalues, it is always diagonalizable.
Think about the conditions required for diagonalization.
Given the matrix A = [[4, 1], [2, 3]], find the eigenvalues and determine whether A is diagonalizable. Justify your reasoning.
Use the characteristic polynomial to derive the eigenvalues.
For the matrix B = [[2, -1], [0, 2]], analyze the multiplicities of eigenvalues and determine its diagonalizability.
Check the number of linearly independent eigenvectors compared to the eigenvalue's multiplicity.
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