If a linear transformation has any two of the properties of being self-adjoint, isometric, or involu

Zain Padilla

Zain Padilla

Answered question

2022-02-14

If a linear transformation has any two of the properties of being self-adjoint, isometric, or involutory, [closed]
Prove that if a linear transformation has any two of the properties of being self-adjoint, isometric, or involutory, then it has the third. (Recall that an involution is a linear transformation A such that A2=1.)

Answer & Explanation

Anabella Olsen

Anabella Olsen

Beginner2022-02-15Added 5 answers

Self adjoint AT=A, isometric AT=A1 involutive A2=I.
self adjoint+isometric implies AT=A=A1 implies A2=I so A is involutive.
self adjoint+involutive AT=A,A2=I implies A=A1=AT so A is isometric.
isometric+involutive AT=A1,A2=I implies A1=A=AT so A is self adjoint.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?