Let V be inner product space. Let e 1 </msub> , . . . , e

George Bray

George Bray

Answered question

2022-06-26

Let V be inner product space.
Let e 1 , . . . , e n an orthonormal basis for V
Let z 1 , . . . , z n an orthonormal basis for V
I have to show that the matrix represents the transformation matrix between e 1 , . . . , e n to z 1 , . . . , z n is unitary.

Answer & Explanation

Bornejecbo

Bornejecbo

Beginner2022-06-27Added 19 answers

Regard the vectors in the orthonormal bases ( e 1 , . . . , e n ) and ( z 1 , . . . , z n ) as column vectors. Then let U e and U z be the matrices where the rows are the transposes of the column vectors e 1 , . . . , e n and z 1 , . . . , z n respectively. Then both U e and U z are unitary, and the matrix which maps between ( e 1 , . . . , e n ) and ( z 1 , . . . , z n ) is going to be given by U e U z 1 , which will be unitary because U e and U z are unitary.

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Linear algebra

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?