Showing papers on "Singular value decomposition published in 1969"
TL;DR: The singular decomposition of a matrix has a variety of uses, especially in statistics as mentioned in this paper, although it is seldom mentioned in books on either matrices or statistics, although some applications are surveyed and some new ones given.
Abstract: It is emphasized that the singular decomposition of a matrix has a variety of uses, especially in statistics, although it is seldom mentioned in books on either matrices or statistics. Some applications are surveyed and some new ones are given.
143 citations
TL;DR: The main idea is to in ter leave composit ions of x and n -x objects and resor t to a lexicographic genera t ion ofComposit ions.
Abstract: p r o c e d u r e Ising (n, x, t, S); i n t e g e r n, x, l; i n t e g e r array S; c o m m e n t Ising generates n-sequences ($1, \" \" , S,) of zeros and ones where x = ~ i ~ S~ and t = ~,-~1 I S~+I S~ I are given. The main idea is to in ter leave composit ions of x and n -x objects and resor t to a lexicographic genera t ion of composit ions. We call these sequences Is ing configurat ions since we believe they first appeared in the s t u d y of the so-called I s ing problem (See Hill [1], Is ing [2]). T he number R(n, x, t) of dist i nc t configurat ions wi th fixed n, x, t is well known [1, 2]:
121 citations