Frequently Asked Questions
When is a matrix diagonalizable?
When it has as many linearly independent eigenvectors as its dimension. Distinct eigenvalues are sufficient; repeated eigenvalues require a check on the eigenspace dimension.
How is diagonalization used?
Powers of A become A to the n equals P D to the n times P inverse - just raise each diagonal entry. Useful for solving recurrences, computing matrix exponentials, and analyzing dynamical systems.
What is a defective matrix?
A matrix that is not diagonalizable: it has a repeated eigenvalue with fewer eigenvectors than the multiplicity. Example: [[1, 1], [0, 1]].
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