Sentence examples for ordered basis from inspiring English sources

Let (mathsf {B}_infty ) be the associated ordered basis of (C(X^omega, Bbbk )).

We now consider the matrix, N, that represents the homomorphism on 1-chains with respect to the ordered basis.

Therefore, ({loggamma_{0},loggamma_{1},loggamma_{3}}loggamma _{3}}) forms a linear ordered basis of (operatorname{Sol}_{1}^{4}) with respect to which (Phi_) can be expressed as a matrix of the form where (varphi_{0}), (varphi_{2}) are integers and (varphi_{1}) is a (2times 2) integer matrix.

Fixing any ordered basis of (C(X^omega, Bbbk )), we get thus a natural faithful representation of the homeomorphism group of (X^omega ) in the group of units of the algebra (mathsf {M}_infty (Bbbk )) of column-finite matrices over (Bbbk ).

Let (b_0<b_1<cdots <b_{d-1}) be the <span class="lh">ordered basis (mathsf {B}).

The new ordered basis for the chain group is (C1, C2, E1, E3, E5, E6).

This paper considers a general multistage assembly system operating on a make to order basis with stochastic manufacturing lead-times.

Denote as above by ((s_1, ldots, s_k )) an ordered free basis of (F_k).

For (k) a positive integer, let (F_k) denote the free group of rank (k), given together with an ordered free basis ((s_1, ldots, s_k)) of generators.

Only 50 will be offered on a build-to-order basis.

Customers pick out clothing samples hanging on racks that Mr. Sabbah fabricates on a made-to-order basis.