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searching for Linear span 31 found (99 total)

Quasi-interior point (330 words) [view diff] exact match in snippet view article find links to article

}}z\leq x\}} is a total subset of X {\displaystyle X} ; that is, if the linear span of [ 0 , x ] {\displaystyle [0,x]} is a dense subset of X . {\displaystyle

Sz.-Nagy's dilation theorem (533 words) [view diff] exact match in snippet view article find links to article

unitary equivalence) when one assumes K is minimal, in the sense that the linear span of ⋃ n ∈ N U n H {\displaystyle \bigcup \nolimits _{n\in \mathbb {N}

Range criterion (580 words) [view diff] exact match in snippet view article find links to article

M=\sum _{i}v_{i}v_{i}^{*}} , the range of M, Ran(M), is contained in the linear span of { v i } {\displaystyle \;\{v_{i}\}} . On the other hand, we can also

Dirac algebra (2,342 words) [view diff] exact match in snippet view article find links to article

, − , − ) {\displaystyle (+,-,-,-)} . The Dirac algebra is then the linear span of the identity, the gamma matrices γ μ {\displaystyle \gamma ^{\mu }}

Fano surface (742 words) [view diff] exact match in snippet view article find links to article

set of lines on F that cuts the disjoint lines Ls and Lt. Consider the linear span of Ls and Lt : it is an hyperplane into P4 that cuts F into a smooth

Canonical bundle (2,548 words) [view diff] exact match in snippet view article find links to article

linearly normal curve of degree 2g − 2 is a canonical curve, provided its linear span is the whole space. In fact the relationship between canonical curves

Compact operator on Hilbert space (4,868 words) [view diff] exact match in snippet view article find links to article

with standard basis {en}. Let Pm be the orthogonal projection on the linear span of {e1, ..., em}. The sequence {Pm} converges to the identity operator

State (functional analysis) (821 words) [view diff] exact match in snippet view article

the theorem. It follows from the above decomposition that A* is the linear span of states. By the Krein-Milman theorem, the state space of M has extreme

Subset (1,734 words) [view diff] exact match in snippet view article find links to article

targets Total subset – Subset T of a topological vector space X where the linear span of T is a dense subset of X Rosen, Kenneth H. (2012). Discrete Mathematics

Dual wavelet (604 words) [view diff] exact match in snippet view article find links to article

k\in \mathbb {Z} } . Such a function is called an R-function if the linear span of { ψ j k } {\displaystyle \{\psi _{jk}\}} is dense in L 2 ( R ) {\displaystyle

Non-RAID drive architectures (1,177 words) [view diff] no match in snippet view article find links to article

filesystem like btrfs; such volumes are usually called "spanned" or "linear | SPAN | BIG". A spanned volume provides no redundancy, so failure of a single

Toral subalgebra (504 words) [view diff] exact match in snippet view article find links to article

{\mathfrak {g}}} must have a nonzero semisimple element, say x; the linear span of x is then a toral subalgebra. Maximal torus, in the theory of Lie

Equations defining abelian varieties (771 words) [view diff] exact match in snippet view article find links to article

The only 'easy' cases are those for d = 1, for an elliptic curve with linear span the projective plane or projective 3-space. In the plane, every elliptic

Min-max theorem (4,542 words) [view diff] exact match in snippet view article find links to article

equalities hold for negative eigenvalues. Proof Let S' be the closure of the linear span S ′ = span ⁡ { u k , u k + 1 , … } {\displaystyle S'=\operatorname {span}

Carathéodory's theorem (convex hull) (2,159 words) [view diff] exact match in snippet view article

..,q_{d}\}} is linearly dependent, then we can use induction on its linear span to eliminate one nonzero term in ∑ n = 1 d w n w 1 + ⋯ + w d q n {\displaystyle

Positive-definite function on a group (1,586 words) [view diff] exact match in snippet view article find links to article

G}\Phi (s)H} where ⋁ {\displaystyle \bigvee } denotes the closure of the linear span. Identify H {\displaystyle H} as elements (possibly equivalence classes)

Petkovšek's algorithm (1,431 words) [view diff] exact match in snippet view article find links to article

e. a generating set for the kernel of the recurrence equation in the linear span of hypergeometric sequences. Petkovšek also showed how the inhomogeneous

Subnormal operator (1,513 words) [view diff] exact match in snippet view article find links to article

h_{i}\in H.} Let K' ⊂ K1 be the subspace that is the closure of the linear span of S. By definition, K' is invariant under B1* and contains H. The normality

Reciprocal lattice (5,496 words) [view diff] exact match in snippet view article find links to article

vectors in Rn. The dual lattice is then defined by all points in the linear span of the original lattice (typically all of Rn) with the property that

Walsh function (2,367 words) [view diff] exact match in snippet view article find links to article

{\displaystyle X_{\gamma }=\{x\in X:R_{t}x=\gamma (t)x\}} . Then X is the closed linear span of the eigenspaces: X = Span ¯ ( X γ , γ ∈ D ^ ) {\displaystyle X={\overline

Normal fan (512 words) [view diff] exact match in snippet view article find links to article

the zero cone. The affine span of face F of P is orthogonal to the linear span of its normal cone, CF. The correspondence between faces of P and cones

Angular momentum operator (6,691 words) [view diff] exact match in snippet view article find links to article

come about from rotating the starting state in every possible way. The linear span of that set is a vector space, and therefore the manner in which the

Spectral theory of normal C*-algebras (3,455 words) [view diff] exact match in snippet view article find links to article

norm topology of B ( H ) {\displaystyle {\mathcal {B}}(H)} ) of the linear span of Im ⁡ π . {\displaystyle \operatorname {Im} \pi .} Then the following

Commutation theorem for traces (2,664 words) [view diff] exact match in snippet view article find links to article

bounded operator; * is the adjoint, in other words (xy, z) = (y, x*z); the linear span of all products xy is dense in A {\displaystyle {\mathfrak {A}}} . The

Sound level meter (6,314 words) [view diff] exact match in snippet view article find links to article

accuracy classes 1 and 2. New in the standard IEC 61672 is a minimum 60 dB linear span requirement and Z-frequency-weighting, with a general tightening of limit

Oscillator representation (21,532 words) [view diff] exact match in snippet view article find links to article

x)}}\end{aligned}}} The operators T(F) have an important non-degeneracy property: the linear span of all vectors T(F)ξ is dense in H {\displaystyle {\mathcal {H}}} . Indeed

Singular integral operators of convolution type (12,881 words) [view diff] exact match in snippet view article find links to article

Hardy space of the circle H2(T) onto H2(R). In fact for |w| < 1, the linear span of the functions f w ( z ) = 1 1 − w z {\displaystyle f_{w}(z)={\frac

Reproducing kernel Hilbert space (6,323 words) [view diff] exact match in snippet view article find links to article

reproducing kernel. Proof. For all x in X, define Kx = K(x, ⋅ ). Let H0 be the linear span of {Kx : x ∈ X}. Define an inner product on H0 by ⟨ ∑ j = 1 n b j K y

Schwarz triangle (10,933 words) [view diff] exact match in snippet view article find links to article

and τ generate a finite or infinite dihedral group; the 2-dimensional linear span U of es and et is invariant under σ and τ, with the restriction of Λ

Glossary of representation theory (5,011 words) [view diff] exact match in snippet view article find links to article

symplectic geometry Peter–Weyl The Peter–Weyl theorem states that the linear span of the matrix coefficients on a compact group G is dense in L 2 ( G )

Symmetric cone (16,613 words) [view diff] exact match in snippet view article find links to article

}} It is straightforward to verify that the real linear span of the diagonal matrices, these matrices and similar matrices with real