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Let and ρ

Let ρ be the initial topology on X induced by C τ ( X ) or, equivalently, the topology generated by the basis of cozero sets in ( X, τ ).

Let ρ, θ, and φ be spherical coordinates for the source point P. Here θ denotes the angle with the vertical axis, which is contrary to the usual American mathematical notation, but agrees with standard European and physical practice.

Let ρ be the correlation coefficient between X 1 and X 2 and let σ i 2 be the variance of X i .

Let ρ denote the number density of electrons, and φ the electric potential.

Let X be a locally compact Hausdorff space equipped with a finite Radon measure μ, and let Y be a σ-compact Hausdorff space with a σ-finite Radon measure ρ.

Let φ: X → Y be a continuous and absolutely continuous function ( where the latter means that ρ ( φ ( E )) = 0 whenever μ ( E ) = 0 ).

Lemma: Let A ∈ C n × n be a complex-valued matrix, ρ ( A ) its spectral radius and ||·|| a consistent matrix norm ; then, for each k ∈ N:

Theorem: Let A ∈ C n × n be a complex-valued matrix and ρ ( A ) its spectral radius ; then

Let π: P → X be a principal G-bundle and let ρ: G → Homeo ( F ) be a continuous left action of G on a space F ( in the smooth category, we should have a smooth action on a smooth manifold ).

Let this property be represented by just one scalar variable, q, and let the volume density of this property ( the amount of q per unit volume V ) be ρ, and the all surfaces be denoted by S. Mathematically, ρ is a ratio of two infinitesimal quantities:

Let ρ: TP / G → M be the projection onto M. The fibres of the bundle TP / G under the projection ρ carry an additive structure.

Let V be a finite-dimensional vector space over a field F and let ρ: G → GL ( V ) be a representation of a group G on V. The character of ρ is the function χ ρ : G → F given by

Let ρ and σ be representations of G. Then the following identities hold:

* Let ρ: G → GL ( n, C ) be a representation.

Let ρ be an irreducible representation of a finite group G on a vector space V of ( finite ) dimension n with character χ.

Let A be an irreducible non-negative n × n matrix with period h and spectral radius ρ ( A ) = r. Then the following statements hold.

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 unitary

Let P − 1 DP be an eigendecomposition of M, where P is a unitary complex matrix whose rows comprise an orthonormal basis of eigenvectors of M, and D is a real diagonal matrix whose main diagonal contains the corresponding eigenvalues.

Let U be a unitary operator on a Hilbert space H ; more generally, an isometric linear operator ( that is, a not necessarily surjective linear operator satisfying ‖ Ux ‖

Let be a complex separable Hilbert space, be a one-parametric group of unitary operators on and be a statistical operator on.

Let U be a strongly continuous 1-parameter unitary group, then there exists a unique self-adjoint operator A such that

Let G be a σ-compact, locally compact topological group and π: G U ( H ) a unitary representation of G on a ( complex ) Hilbert space H. If ε > 0 and K is a compact subset of G, then a unit vector ξ in H is called an ( ε, K )- invariant vector if π ( g ) ξ-ξ < ε for all g in K.

Given a normalized continuous positive definite function f on G, one can construct a strongly continuous unitary representation of G in a natural way: Let F 0 ( G ) be the family of complex valued functions on G with finite support, i. e. h ( g )

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