Examples
of multivariate vectors and matrices of observations
Definition of Transpose
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Multivariate analysis is a
branch of statistics that concerns itself with the analysis of multiple
measurements, made on one or several samples of individuals. For example,
we may wish to measure length, width and weight of a product.
A multiple measurement or observation may be expressed as
x = [4 2 0.6]
referring to the physical properties of length, width and weight respectively.
It is customary to denote multivariate quantities with bold letters. The
collection of measurements on x is called a vector. In this case
it is a row vector. We could have written x as a column vector.
 
If we take several such measurements, we record them in a rectangular
table or array of numbers. For example the X matrix below represents
5 observations, each consisting of three variables.
In this case the number of rows, (n = 5), denotes the number of observations,
and the number of columns, (p = 3) , denotes the number of variables
in the measurement. The rectangular table is an assembly of n row vectors
of length p. This table is called a matrix, or, more specifically, a n
by p matrix. Its name is X. The names of matrices are usually written
in bold, uppercase letters. We could just as well have written X
as a p (variables) by n (measurements) matrix as follows:
A matrix with rows and columns exchanged in this manner is called the transpose
of the original matrix. . |
