Concern the (real) Schur factorization of an n x n matrix A in the form A URU T , 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 ...

If A URU T with U orthogonal then A is similar to R because U is invertible ...

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

Question:

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