Sentence examples for becomes a linear space from inspiring English sources
The set (B(mathcal{C}_{p})) becomes a linear space with coordinatewise additions and scalar multiplication which is linearly isomorphic to the space (mathcal{C}_{p}), and (B(mathcal{C}_{p})) is a complete seminormed space with the seminorm |x|_{B(mathcal{C}_{p})}=lim_{ktoinfty} Bigl(sup _{m,ngeq k} biglvert bigl{ B r,s,t,u xbigr} _{mn} bigrvert Bigr).
It is paranormed by for all where We recall that a paranormed space is total if implies Every total paranormed space becomes a linear metric space with the metric given by It is clear that is a total paranormed space.
Every countably normed linear space becomes a topological linear space when equipped with the topology generated by the neighborhood base consisting of all sets of the form U_{mathfrak{f}, epsilon} = bigcapbigl{ x : x in E ; Vert xVert _{i} < epsilon, iinmathfrak{f} bigr} for some number (epsilon > 0) and finite set (mathfrak{f}) of indices.
One can prove that every countably normed linear space becomes a topological linear space when equipped with the topology generated by the neighborhood base consisting of all sets of the form U_{r, epsilon} = bigl{ x : x in E ; Vert xVert _{1} < epsilon, ldots, |x|_{r} < epsilonbigr} for some number (epsilon > 0) and positive integer r. ([11]).
Note here that MILP-1 becomes a linear programming.
This design problem becomes a linear matrix inequality (LMI) problem.
The worst case becomes a linear time check.
It is easy to see that becomes a normed linear space under the norm. is called the norm of the element (see [3, 4]).
sequences space is a linear space.
is indeed a linear space.
