Where the Poisson problem corresponds to minimization of a quadratic functional over a linear subspace of functions, the free boundary problem corresponds to minimization over a convex set.
42.
Vector subspaces of are equivalent to linear subspaces of the projective space, so it is equivalent to think of the Grassmannian as the set of all linear subspaces of.
43.
Vector subspaces of are equivalent to linear subspaces of the projective space, so it is equivalent to think of the Grassmannian as the set of all linear subspaces of.
44.
A straight line in the projective space, by definition, corresponds to a two-dimensional linear subspace of the ( n + 1 )-dimensional linear space.
45.
Since it is a non-trivial linear subspace of \ mathbf { R } ^ n with less constraints then variables, there is a non-zero solution.
46.
The set of all bilinear maps is a linear subspace of the space ( viz . vector space, module ) of all maps from into " X ".
47.
Where " K " is infinite, a pigeonhole principle proof technique considers the linear subspace generated by two elements and proves that there are only finitely many linear combinations
48.
The set of all one-dimensional linear subspaces of an ( n + 1 )-dimensional linear space is, by definition, an n-dimensional projective space.
49.
For modules and vector spaces, this subset is the only empty-generated submodule ( or 0-dimensional linear subspace ) in each module ( or vector space ).
50.
It's mentioned on the page for dual spaces that if a vector space is topological, the continuous dual space is a linear subspace of the algebraic dual space.
