Linear transformation and it's matrix representation.
- From: "mathlover" <2000korea@xxxxxxxxxxx>
- Date: 4 May 2005 14:27:40 -0700
Hello,
I have question about linear transformation and it's matrix
representation. Let me make a simple example to make clear.
Let T:R2->R2 be a rotation by $ degree. If I choose the standard
ordered basis for R2 then I have theta rotation matrix A
A = [ cos($) -sin($) ; sin($) cos($) ]
Then it's clear AA*=A*A (here * is conjugate adjoint). So my matrix A
is normal. But I rwant to know the normality of T. I tried with
different basis and got the same result. Seems AA*=A*A independent of
choosing basis if T is rotation. How can I show rotation T is normal?
Is it related with normality of matrix representation.
.
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