ey (t) z 2,144 (+) + ay odo (5) du. ia icio core ey dp C6) T Tr, (+) (1) 
where T, (+) is a residual vector. 
A set of such linear combinations can in matrix notation be 
written as 
6 = 331,337 DA 
= à,0,+ R5Q5 + ++... + aq. +R (2) 
The matrix C is known, while the vectors a. and a; are to 
be determined. In cases when the rank of the matrix C is 
less than or equal to the number of base functions, the 
vectors a; and q, may be chosen in such a way that the 
residual matrix R is equal to zero. 
There is an infinite number of solutions to this equation 
system. The solution chosen in the K-L expansion is the one 
where the base functions d; are normalized and orthogonal 
and where the vectors a, are orthogonal. This can be 
expressed as 
3; d; = n-1 (3a) 
di d; 0 , when i * j (3b) 
8 a, =. 0 ,~when i #_3J (3c) 
It is shown (Rao, 1965), that this solution has some very 
favourable characteristics. 
The residual matrix R is expressed as 
i stat 5ra-7 = =T 
Rz Cu 244) = 8505 = +... - & (4) 
The size of the elements of a matrix can be expressed by its 
Euclidian norm. The norm IRI is then estimated by 
IRI* te (e; 
i j 
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