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Here VR is a real subspace of V, i.e. a subspace of V considered as a vector space over the real numbers. If V has complex dimension n (real dimension 2n)...

linear subspace or vector subspace is a vector space that is a subset of some larger vector space. A linear subspace is usually simply called a subspace when...

= Tp(M) ⊕ (Tp(M))∗. The complex analog to a Lagrangian subspace is a real subspace, a subspace whose complexification is the whole space: W = V ⊕ J V...

mathematics, a subspace of a topological space X is a subset S of X which is equipped with a topology induced from that of X called the subspace topology (or...

SubSpace is a 2D space shooter video game created in 1995 and released in 1997 by Virgin Interactive which was a finalist for the Academy of Interactive...

In mathematics, an invariant subspace of a linear mapping T : V → V i.e. from some vector space V to itself, is a subspace W of V that is preserved by...

v\mapsto v\otimes 1.} The vector space V may then be regarded as a real subspace of VC. If V has a basis { ei } (over the field R) then a corresponding...

imaginary point. A subspace of a projective space is real if it is spanned by real points. Every imaginary point belongs to exactly one real line, the line...

linear subspace (vector subspace) of a vector space produces an affine subspace of the vector space. One commonly says that this affine subspace has been...

if and only if all its coefficients are zero. Linear subspace A linear subspace or vector subspace W of a vector space V is a non-empty subset of V that...

{\displaystyle A} can also be called a meagre subspace of X {\displaystyle X} , meaning a meagre space when given the subspace topology. Importantly, this is not...

functions and pointwise scalar multiplication. All sequence spaces are linear subspaces of this space. Sequence spaces are typically equipped with a norm, or...

numbers with 1 is a real line within the algebra. For example, in the complex plane z = x + iy, the subspace {z : y = 0} is a real line. Similarly, the...

is an open dense subspace of a compact Hausdorff space having at most one point more than X. A nonempty compact subset of the real numbers has a greatest...

of non-negative real numbers). Geometrically, Bessel's inequality implies that the orthogonal projection of x onto the linear subspace spanned by the fi...

{R} ,} endowed with a complex structure; that is, there exists a real vector subspace X R {\displaystyle X_{\mathbb {R} }} such that we can (formally)...

subspaces: its Euclidean subspaces and its linear subspaces. Linear subspaces are Euclidean subspaces and a Euclidean subspace is a linear subspace if...

dimension n is defined as the set of the vector lines (that is, vector subspaces of dimension one) in a vector space V of dimension n + 1. Equivalently...

technology is becoming feasible. In the Star Trek fictional universe, subspace is a feature of space-time that facilitates faster-than-light transit,...

to itself. Let h 0 ∗ {\displaystyle {\mathfrak {h}}_{0}^{*}} be the real subspace of h ∗ {\displaystyle {\mathfrak {h}}^{*}} generated by the roots of...