Quote:
Originally Posted by Kat-M  Let T be a linear transformation from R^2 to R^2. and T is represented by the matrix B=
[(1/5)^(1/2) -2(1/5)^(1/2)]
[2(1/5)^(1/2) (1/5)^(1/2)]
with respect to the stantard basis of R^2.
a) Is T isometry?
b) does R^2 have an orthonormal basis for eigenvectors of T?
i can do a) but need help on b). i dont really understand what it is asking. is it asking to find an orthonormal basis for eigen space of T? |
It asks whether there's an orthonormal base for
made out of eigenvectors of
What they want you to see is that, if you were working with complex numbers instead of real numbers, b) would hold -by the spectral theorem for Unitary Transformations-, but here it may not ( Try !
).