Let the Matrix
satisfy the conditions of the Perron-Frobenius Theorem and the
Matrix
satisfy

for , 2, ..., . Then any Eigenvalue of satisfies the inequality with the equality sign holding only when there exists an Matrix (where is the Kronecker Delta) and

**References**

Gradshteyn, I. S. and Ryzhik, I. M. *Tables of Integrals, Series, and Products, 5th ed.* San Diego, CA:
Academic Press, p. 1121, 1979.

© 1996-9

1999-05-26