Nonnegative matrices are important in a variety of applications and have a number of attractive mathematical properties. Together with positive
semidefinite matrices, they therefore serve as a natural generalization of nonnegative
real numbers (Johnson 1981). The most fundamental properties of nonnegative matrices
require fairly advanced mathematics and were established by Perron (1907) and Frobenius
(1912).
Berman, A. and Plemmons, R. J. Nonnegative Matrices in the Mathematical Sciences. SIAM, 1994.Carlson, D.
Book review. "Nonnegative Matrices in the Mathematical Sciences. By Abraham
Berman and Robert J. Plemmons. Academic Press, New York, 1979." SIAM
Review23, 409-410, 1981.Frobenius, G. "Über Matrizen
aus nicht negativen Elementen." S.-B. Preuss. Akad. Wiss. (Berlin). pp. 456-477,
1912.Gantmacher, F. R. The Theory of Matrices, Vols. 1
and 2. New York: Chelsea, New York, 1959.Johnson, C. R. Book
review. "Nonnegative Matrices in the Mathematical Sciences, by Abraham
Berman and Robert J. Plemmons, Academic Press, New York, 1979." Bull.
Amer. Math. Soc.6, 233-235, 1981.Perron, O. "Zur theorie
der matrizen." Math. Ann.64, 248-263, 1907.Senta,
E. Nonnegative Matrices. New York: Wiley, 1973.Taussky, O. Eigenvalues
of Finite Matrices. New York: McGraw-Hill, 1962.Varga, R. S.
Matrix Iterative Analysis. Englewood Cliffs, NJ: Prentice-Hall, 1962.Wielandt,
H. "Unzerlegbare, nicht negative matrizen." Math. Z.52,
642-648, 1950.
for which each matrix element is a nonnegative
number, i.e., 
for all 
,
.
