Author(s)

Morteza Seddighin^*

Indiana University East, Richmond, USA.

In this paper we show that the author’s Two Nonzero Lemma (TNCL) can be applied to present a simple proof for a very useful equality which was first proved by Karl Gustafson in 1968. Gustafson used Hilbert space methods, including convexity of the Hilbert space norm, to prove this identity which was the basis of his matrix trigonometry. By applying TNCL, we will reduce the problem to a simple problem of ordinary calculus.

Matrix Trigonometry

Seddighin, M. (2017) Two Nonzero Component Lemma and Matrix Trigonometry. Advances in Linear Algebra & Matrix Theory, 7, 1-6. doi: 10.4236/alamt.2017.71001.