Question

if A and B ate hermitian ,show that BAB and ABA are hermitian​

Answer 1

Answer:

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Step-by-step explanation:

From the definition of the conjugate transpose of a matrix AA, denoted by A†A†, you can show that if AA and BB are two square matrices, then (AB)†=B†A†(AB)†=B†A†.

Applying this property twice to ABAABA yields: (ABA)†=(BA)†A†=A†B†A†=ABA(ABA)†=(BA)†A†=A†B†A†=ABA, where the last equality follows from the assumption that AA and BB are both Hermitian matrices. Hence ABAABA is also Hermitian.

Answer 2

Answer:

Hermitian Matrix is a special matrix, which is same as its conjugate transpose as expressed below.

A=A'.

Property of the transpose of reverse

(AB)'=B' A'.

Applying property of the transpose in the given expression

( BAB)'= B'A'B'

B'A'B'=BAB.

Similar we can write

(ABA)'= A' B'A'.

A'B'A'=ABA.

Hence proved that BAB and ABA are Hermitian matrices.