P-1.18 Let A₁ = B-¹C and A2 = CB where C is a Hermitian matrix and B is a Hermitian Positive Definite matrix. Are A₁ and A₂ Hermitian in general? Show that A₁ and A₂ are Hermitian (self-adjoint) with respect to the B-inner product.

Linear Algebra: A Modern Introduction
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ISBN:9781285463247
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Chapter4: Eigenvalues And Eigenvectors
Section4.6: Applications And The Perron-frobenius Theorem
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P-1.18 Let A₁ = B-¹C and A2 = CB where C is a Hermitian matrix and B is a Hermitian
Positive Definite matrix. Are A₁ and A₂ Hermitian in general? Show that A₁ and A₂ are
Hermitian (self-adjoint) with respect to the B-inner product.
Transcribed Image Text:P-1.18 Let A₁ = B-¹C and A2 = CB where C is a Hermitian matrix and B is a Hermitian Positive Definite matrix. Are A₁ and A₂ Hermitian in general? Show that A₁ and A₂ are Hermitian (self-adjoint) with respect to the B-inner product.
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