Biology Reference
In-Depth Information
CHAPTER 2
PART 2
Statistical and Mathematical
Preliminaries for Landmark
Coordinate Data
We now introduce some statistical and mathematical concepts that are
important for the statistical analysis of landmark data, whether con-
ducting measurement error studies or comparing two forms or shapes.
Matrix algebra is an essential mathematical tool in multivariate sta-
tistical analysis. It is particularly useful in the statistical analysis of
landmark coordinate data. We strongly recommend that everyone read
this part carefully. Readers who are mathematically and statistically
challenged should at least try to familiarize themselves with the nota-
tion and some of the essential statistical and mathematical
terminology introduced here, as it is used throughout the remaining
chapters.
2.6 Introduction to matrix algebra
In this section, we introduce some of the basic ideas of matrix algebra.
This is by no means a complete tutorial in matrices and their uses in
multivariate analysis. For such a review, we refer the reader to Searle
(1982). There are also many mathematical topics on matrix algebra,
e.g., Barnett (1990). The inquisitive reader may look to these sources
for more details. The choice of topics covered here is dictated by our
requirements for exposition of the use of matrix algebra in the analy-
sis of landmark data.
1)
Definition of a matrix:
A matrix is a rectangular array of ele-
ments arranged in rows and columns.
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