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 10 May 2008 13:52 PRACTICAL PROBLEMS OF MATRIX CALCULATION |
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PRACTICAL PROBLEMS OF MATRIX
CALCULATION*
HAROLD HOTELLING
UNIVERSITY OF NORTH CAROLINA
1. Introduction
Statistical analysis involving any considerable number of variates leads
usually to calculations which, if not well organized and conducted with the
help of suitable machines, may be excessively laborious. The great possibilities
opened up by the advances in the theory of multivariate statistical analysis
will gain in accessibility as computational methods improve in this domain.
The computations most needed involve matrices. This is true, for example, in
the method of least squares and in calculating multiple correlation coefficients;
it is true in the calculation of the generalized Student ratio and figurative distance
that has become the modern substitute for Karl Pearson's coefficient of
racial likeness; also in studying the relations between two or more sets of
variates, and the principal components of one set.
The same computational problems arise also in many fields outside of statistics-
if indeed we can speak of any field as being outside of statistics! Thus
the study of vibrations in airplanes and other machines and structures; the
analysis of stresses and strains in bridges, of electrical networks, of mass spectroscopy
of petroleum products; and many other subjects of importance require
calculations of the same kinds as multivariate analysis in statistics.
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