- #1
Treadstone 71
- 275
- 0
"Let T be a linear transformation on a finite dimensional real vector space V. Show that T is diagonalisable if and only if there exists an inner product on V relative to which T is self-adjoint."
The backward direction is easy. As for the forward direction, I don't understand how given an arbitrary vector space, you can go about defining an inner product without knowing something more about it.
The backward direction is easy. As for the forward direction, I don't understand how given an arbitrary vector space, you can go about defining an inner product without knowing something more about it.