HILBERT MATRIX

HILBERT, DAVID.

Ein Beitrag zur Theorie des Legendre'schen Polynoms.

Berlin, Stockholm, Paris, Almqvist & Wiksell, 1894. 4to. Bound in contemporary half cloth with gilt lettering to spine. In "Acta Mathematica", Vol, 18, 1894. Entire volume offered. Stamps to title page and light wear to extremities, otherwise a fine and clean copy. Pp. 155-59.[Entire volume: (4), 421, (2) pp].

First printing of Hilbert's paper in which he introduced The Hilbert Matrix. In linear algebra, a Hilbert matrix is a square matrix with entries being the unit fractions. The Hilbert matrix is symmetric and positive definite and is also totally positive (meaning the determinant of every submatrix is positive). The Hilbert matrix is an example of a Hankel matrix.

Order-nr.: 49646