TABLE OF CONTENTS Many tricks or treats associated with the Hilbert matrix may seem rather frightening or fascinating.
MAN-DUEN CHOI, Tricks or Treats with the Hilbert Matrix (1983)
I start by looking at a 2 by 2 matrix. Sometimes I look at a 4 by 4 matrix. That's when things get out of control and too hard. Usually 2 by 2 or 3 by 3 is enough, and I look at them, and I compute with them, and I try to guess the facts. First, think of a question. Second, I look at examples, and then third, guess the facts.
PAUL R. HALMOS [23] (1991)
When people look down on matrices, remind them of great mathematicians such as Frobenius, Schur, C. L. Siegel, Ostrowski, Motzkin, Kac, etc., who made important contributions to the subject.
OLGA TAUSSKY, How I Became a Torchbearer for Matrix Theory (1988)
[23]From interviews by Albers in [10, 1991].
Ever since the first computer programs for matrix computations were written in the 1940s, researchers have been devising matrices suitable for test purposes and investigating the properties of these matrices. In the 1950s and 1960s it was common for a whole paper to be devoted to a particular test matrix: typically its inverse or eigenvalues would be obtained in closed form.
Early collections of test matrices include those of Newman and Todd [891, 1958] and Rutishauser [1006, 1968]; most of Rutishauser's matrices come from continued fractions or moment problems. Two well-known books...
