Let T be a linear operator on the finite-dimensional vector space V over the field F.

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 us now regard D as a linear operator on the subspace V.

Let V, W and X be three vector spaces over the same base field F. A bilinear map is a function

Theorem: Let V be a topological vector space

Let us assume the bias is V and the barrier width is W. This probability, P, that an electron at z = 0 ( left edge of barrier ) can be found at z = W ( right edge of barrier ) is proportional to the wave function squared,

If V is a real vector space, then we replace V by its complexification V ⊗< sub > R </ sub > C and let g denote the induced bilinear form on V ⊗< sub > R </ sub > C. Let W be a maximal isotropic subspace, i. e. a maximal subspace of V such that g |< sub > W </ sub > = 0.

The singles " So Far Away " and " Price to Play " came with two unreleased tracks, " Novocaine " and " Let It Out ", which were released for the special edition of the group's Chapter V, which came out in late 2005.

In early November 2005, Staind released the limited edition 2-CD / DVD set of Chapter V. The set included several rarities and fan favorites — music videos ; a complete, 36-page booklet with exclusive artwork ; an audio disc with an acoustic rendition of " This is Beetle "; the original, melodic rendition of " Reply "; the previously released B-side singles " Novocaine " and " Let It Out "; and live versions of " It's Been Awhile " and " Falling ", among many others.

Let u, v be arbitrary vectors in a vector space V over F with an inner product, where F is the field of real or complex numbers.

Let V and W be vector spaces ( or more generally modules ) and let T be a linear map from V to W. If 0 < sub > W </ sub > is the zero vector of W, then the kernel of T is the preimage of the zero subspace

Let V be a vector space over a field K, and let be a quadratic form on V. In most cases of interest the field K is either R, C or a finite field.

Let U and V be two open sets in R < sup > n </ sup >.

Suppose that in a mathematical language L, it is possible to enumerate all of the defined numbers in L. Let this enumeration be defined by the function G: W → R, where G ( n ) is the real number described by the nth description in the sequence.

Let us take a hypothetical single scan line, with B representing a black pixel and W representing white:

Let ω be a generator of W ′< sup > k </ sup >.

A possible definition of spoiling based on vote splitting is as follows: Let W denote the candidate who wins the election, and let X and S denote two other candidates.

Let V be a vector space over the field K, and let W be a subset of V.

# Let p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) and q = ( q < sub > 1 </ sub >, q < sub > 2 </ sub >) be elements of W, that is, points in the plane such that p < sub > 1 </ sub > = p < sub > 2 </ sub > and q < sub > 1 </ sub > = q < sub > 2 </ sub >.

# Let p = ( p < sub > 1 </ sub >, p < sub > 2 </ sub >) be an element of W, that is, a point in the plane such that p < sub > 1 </ sub > = p < sub > 2 </ sub >, and let c be a scalar in R. Then cp = ( cp < sub > 1 </ sub >, cp < sub > 2 </ sub >); since p < sub > 1 </ sub > = p < sub > 2 </ sub >, then cp < sub > 1 </ sub > = cp < sub > 2 </ sub >, so cp is an element of W.

" Of course, he was a formidable adversary ," Westmoreland told correspondent W. Thomas Smith, Jr. " Let me also say that Giap was trained in small-unit, guerrilla tactics, but he persisted in waging a big-unit war with terrible losses to his own men.

Let V and W be two vector spaces, and let W * be the dual space of W.

Let U, V, and W be vector spaces over the same field with given bases, S: V → W and T: U → V be linear transformations and ST: U → W be their composition.

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 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 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??