- #1

- 8

- 0

**1. Homework Statement**

Suppose T is a linear operator on a finite dimensional vector space V, such that every subspace of V with dimension dim V-1 is invariant under T. Prove that T is a scalar multiple of the identity operator.

**3. The Attempt at a Solution**

I'm thinking of starting by letting U and W be subspaces of V with dim U = dim W = dim V-1

This means that U and W are invariant under T. Good start? Where do i go from there to show that T is a scalar multiple of the identity operator?