Grade 12IIT JEE Entrance Exam
If A is a hermitian matrix .then prove that adjA is also hermitian.
1 Answer
Latika Leekha
Hello student,
Let A be hermitian.
Then, Aθ = A.
So, now to prove that adj A is also hermitian, we need to prove that (adj A)θ = adj A.
Consider, (adj A)θ = adj Aθ (follows by property)
= adj A (Since, Aθ = A)
and so, adj A is hermitian.
Let A be hermitian.
Then, Aθ = A.
So, now to prove that adj A is also hermitian, we need to prove that (adj A)θ = adj A.
Consider, (adj A)θ = adj Aθ (follows by property)
= adj A (Since, Aθ = A)
and so, adj A is hermitian.
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