Help


[permalink] [id link]
+
Page "Bra-ket notation" ¶ 148
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

Let and be
Let the open enemy to it be regarded as a Pandora with her box opened ; ;
Let every policeman and park guard keep his eye on John and Jane Doe, lest one piece of bread be placed undetected and one bird survive.
`` Let him be now ''!!
Let us assume that it would be possible for an enemy to create an aerosol of the causative agent of epidemic typhus ( Rickettsia prowazwki ) over City A and that a large number of cases of typhus fever resulted therefrom.
Let T be a linear operator on the finite-dimensional vector space V over the field F.
Let p be the minimal polynomial for T, Af, where the Af, are distinct irreducible monic polynomials over F and the Af are positive integers.
Let Af be the null space of Af.
Let N be a linear operator on the vector space V.
Let T be a linear operator on the finite-dimensional vector space V over the field F.
Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.
Let N be a positive integer and let V be the space of all N times continuously differentiable functions F on the real line which satisfy the differential equation Af where Af are some fixed constants.
Let Q be a nonsingular quadric surface bearing reguli Af and Af, and let **zg be a Af curve of order K on Q.
Let us take a set of circumstances in which I happen to be interested on the legislative side and in which I think every one of us might naturally make such a statement.
Let the state of the stream leaving stage R be denoted by a vector Af and the operating variables of stage R by Af.
Let this be denoted by Af.
Let it be granted then that the theological differences in this area between Protestants and Roman Catholics appear to be irreconcilable.
Let not your heart be troubled, neither let it be afraid ''.
The same God who called this world into being when He said: `` Let there be light ''!!
For those who put their trust in Him He still says every day again: `` Let there be light ''!!
Let us therefore put first things first, and make sure of preserving the human race at whatever the temporary price may be ''.
Let her out, let her out -- that would be the solution, wouldn't it??

Let and dual
Let H be a Hilbert space, and let H * denote its dual space, consisting of all continuous linear functionals from H into the field R or C. If x is an element of H, then the function φ < sub > x </ sub >, defined by
Let X be a normed topological vector space over F, compatible with the absolute value in F. Then in X *, the topological dual space X of continuous F-valued linear functionals on X, all norm-closed balls are compact in the weak -* topology.
Let V and W be two vector spaces, and let W * be the dual space of W.
Let V be a vector space over a field k. The core of the contraction operation, and the simplest case, is the natural pairing of V with its dual vector space V *.
Let denote this topological vector space, called the strong dual of X.
Let V be a real vector space of dimension n and V < sup >∗</ sup > its dual space.
Let V < sup >∗</ sup > be the dual vector space of V. In other words, V < sup >∗</ sup > is the set of all linear maps from V to C with addition defined over it in the usual linear way, but scalar multiplication defined over it such that for any z in C, ω in V < sup >∗</ sup > and X in V. This is usually rewritten as a contraction with a sesquilinear form 〈·,·〉.
Let Λ be the lattice in R < sup > d </ sup > consisting of points with integer coordinates ; Λ is the character group, or Pontryagin dual, of R < sup > d </ sup >.
Precisely, let T be a triangulation of an n-manifold M. Let S be a simplex of T. We denote the dual cell ( to be defined precisely ) corresponding to S by DS.
Let G be a locally compact abelian group and G < sup >^</ sup > be the Pontryagin dual of G. The Fourier-Plancherel transform defined by
Let E < sub > i </ sub > be a basis of sections of TG consisting of left-invariant vector fields, and θ < sup > j </ sup > be the dual basis of sections of T < sup >*</ sup > G such that θ < sup > j </ sup >( E < sub > i </ sub >) = δ < sub > i </ sub >< sup > j </ sup >, the Kronecker delta.
Let V be a vector space, and V < sup >*</ sup > its dual.
Let p be a point of P < sup > 2 </ sup > and ℓ a line of the dual projective plane.
Let B be an arbitrary Banach space, and let B < sup >*</ sup > be its dual, that is, the space of bounded linear functionals on B.

Let and space
* Theorem Let X be a normed space.
* Corollary Let X be a reflexive normed space and Y a Banach space.
* Corollary Let X be a reflexive normed space.
Let be a Hilbert space and is a vector in.
Let S be a vector space over the real numbers, or, more generally, some ordered field.
Let M be a smooth manifold and let x be a point in M. Let T < sub > x </ sub > M be the tangent space at x.
Let x, y, z be a system of Cartesian coordinates in 3-dimensional Euclidean space, and let i, j, k be the corresponding basis of unit vectors.
Let X be a topological space, and let x < sub > 0 </ sub > be a point of X.
Theorem: Let V be a topological vector space
Let be a metric space.
Let denote the space of scoring functions.
Let X be a measurable space, let μ be a measure on X, and let N be a measurable set in X.
These assumptions can be summarised as: Let ( Ω, F, P ) be a measure space with P ( Ω )= 1.
Let X be a locally compact Hausdorff space.

0.657 seconds.