The Multivariate Linear Functional Relationship

Abstract

In this chapter we shall consider the functional relationship,

$$B^T \xi = 0\quad \quad (i = 1,2,..,n)$$

(3.1)

$$\textup{B}^\textup{T} \xi = 0 (\textup{i}=1, 2, .., \textup{n})$$

where B(β_jk) is a (p × m) matrix of coefficients which determine the p-m dimensional subspace of the p-dimensional ξ space defined by (3.1). Some of these coefficients can be free and unknown parameters whereas others have to be fixed in advance in order to ensure a unique relationship between the free parameters and the subspace they define, i.e. to ensure identifiability (cf. section II).