Concern the (real) Schur factorization of an n x n matrix A in the form A =

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Concern the (real) Schur factorization of an n x n matrix A in the form A = URUT, where U is an orthogonal matrix and R is an n x n upper triangular matrix.1

Show that if A admits a (real) Schur factorization, A D  URUT , then A and R have the same characteristic polynomial.  Deduce that A has n real eigenvalues, counting multiplicities.

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Linear Algebra And Its Applications

ISBN: 9781292351216

6th Global Edition

Authors: David Lay, Steven Lay, Judi McDonald

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