hermitian

if A and B are hermitian prove AB-BA IS SKEW HERMIITAN

2 Answers

Hermitian matrix implies, matrix is equal to its conj. transpose
so, A=A^~ and B=B^~........(let X^~ denote conj. transpose)

AB-BA = K
K^~=(AB-BA)^~=(AB)^~-(BA)^~
K^~=B^~A^~-A^~B^~
K^~=BA-AB=-(AB-BA)=-K

MY.............MY...............I KNEW WRONG DEFINITION OF HERMITIAN...................

THANX SAMARTH..........

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