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4 cards from this section. Quick, good the night before a test.
What is the first step to find the basis of eigenvectors for a given matrix?
Think about how you set up the determinant.
What does the eigenspace correspond to?
Consider what defines a set of vectors for a given λ.
What do you solve to find eigenvalues for matrix A?
What condition makes the determinant zero?
True or False: The eigenspace for an eigenvalue includes only the zero vector.
Think about how many vectors make up an eigenspace.
Given the 2x2 matrix A = [[1, 2], [0, 1]], calculate its eigenvalues and corresponding eigenvectors, discussing the implications of your findings.
What form will the characteristic polynomial take?
For the matrix B = [[4, 1], [0, 4]], derive the eigenvectors and explain the relevance of the result for a repetitive eigenvalue.
How does the multiplicity of eigenvalues affect the linear independence of eigenvectors?
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