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Non diagonalization test
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Test for non diagonalizability
In this video, I state and prove the converse to the ultimate test of diagonalization: namely, a matrix is diagonalizable (if and) only if for every eigenvalue, the algebraic multiplicity equals the geometric multiplicity. Intuitively, this means if there aren't enough eigenvectors, then the matrix isn't diagonalizable. This is useful to check if a matrix is not diagonalizable.
In this video, I state and prove the converse to the ultimate test of diagonalization: namely, a matrix is diagonalizable (if and) only if for every eigenvalue, the algebraic multiplicity equals the geometric multiplicity. Intuitively, this means if there aren't enough eigenvectors, then the matrix isn't diagonalizable. This is useful to check if a matrix is not diagonalizable.
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