  Based on a suggestion of Richard Hamilton, we give an alternate proof of his
matrix Harnack inequality for solutions of the Ricci flow with positive
curvature operator. This Harnack inequality says that a certain endomorphism,
consisting of an expression in the curvature and its first two covariant
derivatives, of the bundle of 2-forms Whitney sum 1-forms is nonnegative. The
idea is to consider the 2-form which minimizes the associated quadratic form to
obtain a symmetric 2-tensor. A long but straightforward computation implies
this 2-tensor is a subsolution to heat-type equation. A standard application of
the maximum principle implies the result.
