can anybody help me with this question?

Show that if a matrix A is both triangular and unitary, then it is diagonal.

thanks

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- Apr 13th 2009, 01:30 AMBucephalusUnitary and triangular = diagonal matrix
can anybody help me with this question?

Show that if a matrix A is both triangular and unitary, then it is diagonal.

thanks - Apr 13th 2009, 03:15 AMNonCommAlg
i'll assume that the matrix is upper triangular. the lower triangular case is the same. proof is by induction over : for it's easy. now if where

is the complex conjugate of then we'll have but and therefore now apply the induction hypothesis for the

matrix to finish the proof. - Apr 13th 2009, 04:05 AMBucephalus
then we'll have but and therefore

I don't really understand how

and - Apr 13th 2009, 04:10 AMBucephalusQuote:

and

is the element multiplied by the

element.

Is that correct?

i'm going to try that on paper. - Apr 13th 2009, 04:18 AMBucephalus
SOrry, I mean the conjugate of the element.

not element.

Don't worry,I will do some paper work here.

I think I'm starting to understand some of your proof using a 2X2 Identity matrix.

thanks for your response.