The Haar condition holds for a set of vectors in Euclidean n-space if every set
of 
vectors is
linearly independent (Cheney 1999). Expressed
otherwise, each selection of 
vectors from such a set
is a basis for n-space.
In the function-space setting, let 
be a vector space of finite
dimension 
consisting of real-valued continuous functions on an interval ![[a,b]](/images/equations/HaarCondition/Inline5.svg)
with 
. For a basis 
of 
and 
distinct points ![x_1,...,x_n in [a,b]](/images/equations/HaarCondition/Inline10.svg)
, let the matrix 
. The Haar condition requires the
determinant to satisfy
 |
for every such choice of points. Equivalently, every nonzero function in 
has at most 
distinct zeros in ![[a,b]](/images/equations/HaarCondition/Inline14.svg)
(Powell 1981, pp. 313-316). Thus the evaluation vectors 
at 
distinct arguments form a basis
for 
.
A system of functions satisfying the Haar condition is sometimes termed a Tchebycheff system (Cheney 1999).
