H 113 Use The Jordan Form To Prove Schur S Lemma If A Is An N X N Matrix Over C Then There Exists An N X N Unitary Ma 1 (26.79 KiB) Viewed 51 times
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[H]113 Use the Jordan form to prove Schur's Lemma: if A is an n x n matrix over C, then there exists an n x n unitary matrix Q and an upper triangular matrix U such that A = QUQ*; moreover, the diagonal of U consists of the eigenvalues of A, repeated according to multiplicity. Note: If this result is proved without Jordan forms, it can then be used as the basis of an alternative proof that every square matrix has a Jordan form.
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