X] becomes too badly conditioned we compute a new orthogonal basis.

By choosing a representation of the multivariate polynomials in terms of an orthogonal basis with respect to a discrete inner product for a geometry, numerical problems are avoided for larger point sets.

i]} consists of an

orthogonal basis of matrix space [R.

In consequence, the elements of the orthogonal basis [([e.

Mortici: A numerical construction of an orthogonal basis in the Sobolev space [H.

can be represented in terms of this

orthogonal basis as

Exploiting this equivalence there is in principle no difference between manipulations in the spin space of neutrons with the

orthogonal basis {|[up arrow]>, |[down arrow]>} as eigenstates of [[sigma].

In addition, both articles use the same illustration for their first figure: a three-dimensional coordinate system where index terms are depicted as orthogonal basis vectors and documents are plotted as vectors in the space of term weights.

Modeling variables as orthogonal basis vectors suggests that those variables either are or should be treated as statistically independent of one another.

s] are the normal

orthogonal basis for range R(R) and null space N(R) of R, espectively.

This paper solves the problem of finding, in a least squares sense, the coefficients of a series expansion of a function in terms of a chosen

orthogonal basis from the knowledge not of the function itself but from the action of a linear operator upon it.

Since the spectrum of A is simple, its eigenfunctions form an

orthogonal basis in the Hilbert space.