ABSTRACT
The conditions of biorthogonality we can be also written in matrix no tation in a fashion reminding the similar equations in the scalar case:
(*(x - k), * (s - /)) = 6{k - 1)1, - k), 4 (x - /)) = 0 (9 (x - k), 9 (x - I)} = S(k - 1)1 ($(x - k), 9 (x - I)) = 0. (7)
Here, ( . , . ) does not stand for a proper inner product. Rather, it is a vec tor generalization of the L2 inner product, (f ( x ), = J f ( x )(9(%))* dx (* denotes the ordinary conjugated transpose). The value yielded thus is an r x r matrix.
