Criterion for linear independence of functions
نویسنده
چکیده
where T1, . . . , Tn, S1, . . . , Sn : [a, b] → R. (2) Suppose K 6= 0. Then we may consider each of the systems {T1, . . . , Tn}, {S1, . . . , Sn} linearly independent. Indeed, starting from an expression of kind (1), we consequently reduce the number of items while it is needed. Assume that we need to express the functions (2) in terms of K. In order to do it, we find such points (a proof of existence and a way of finding will follow) t1, . . . , tn, s1, . . . , sn ∈ [a, b], (3) that the square matrices T = [Tj(ti)], S = [Sj(si)] of size n are nonsingular, write out the identities
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