(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Let T: R3 - R3 be the linear operator given by

T = -y + z

-x + z

x + y

Find a basis B' for R3 relative to which the matrix for T is diagonal using the standard basis B for R3.

2. Relevant equations

[T]_{B'}= P^{-1}[T]_{B}P

3. The attempt at a solution

I find the standard matrix for T to be

0 -1 1

-1 0 1

1 1 0

The characteristic equation of which, I find to be

(lambda)^3 -3(lambda) + 2 = 0

Which has no real solutions? What can I do?

Thanks

Derryck

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Diagonal bases in transformations

**Physics Forums | Science Articles, Homework Help, Discussion**