Let V be a finite-dimensional vector space over an algebraically closed field F, e.g., the field of complex numbers.

Let A be a complex unital Banach algebra in which every non-zero element x is invertible ( a division algebra ).

Let x < sub > 0 </ sub >, ...., x < sub > N-1 </ sub > be complex numbers.

The saying " Let your Yes be Yes and your No be No " from James 5: 12 is interpolated into a sayings complex from Matthew 5: 34, 37.

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 P < sup >− 1 </ sup > 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 be a list of n linearly independent vectors of some complex vector space with an inner product.

Let K be the set C of all complex numbers, and let V be the set C < sub > C </ sub >( R ) of all continuous functions from the real line R to the complex plane C.

Let be a complex rational function from the plane into itself, that is,, where and are complex polynomials.

Consider an open subset U of the complex plane C. Let a be an element of U, and f: U

Let be an open subset of the complex plane, a point of and a holomorphic function defined on the set.

Let k be a field ( such as the rational numbers ) and K be an algebraically closed field extension ( such as the complex numbers ), consider the polynomial ring kX < sub > n </ sub > and let I be an ideal in this ring.

Let x, y, z be complex numbers, and let a, b be real numbers.

Let q be a prime number, s a complex variable, and define a Dirichlet L-function as

Let be the space of all complex valued Taylor series

Let B be a complex Banach algebra containing a unit e. Then we define the spectrum σ ( x ) ( or more explicitly σ < sub > B </ sub >( x )) of an element x of B to be the set of those complex numbers λ for which λe − x is not invertible in B.

Let X be a compact complex manifold of complex dimension n. Then X is an orientable smooth manifold of real dimension 2n, so its cohomology groups lie in degrees zero through 2n.

Let Z be a complex submanifold of X of dimension k, and let i: Z → X be the inclusion map.

Let X be a projective complex manifold.

:: Let X be a projective complex manifold.

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 us look at the heavy-electrical-goods industry in which General Electric, Westinghouse and a number of other manufacturers were recently convicted of engaging in a conspiracy to rig prices and allocate the market.

* Let Q be a set enclosed between two step regions S and T. A step region is formed from a finite union of adjacent rectangles resting on a common base, i. e. S ⊆ Q ⊆ T. If there is a unique number c such that a ( S ) ≤ c ≤ a ( T ) for all such step regions S and T, then a ( Q )

They have appeared together in a number of films, including Edie & Pen ( 1996 ), American Perfekt ( 1997 ) and Let the Devil Wear Black ( 1999 ).

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.

Peaking at number six in the UK, the album yielded the hits " Day-In, Day-Out " ( his 60th single ), " Time Will Crawl ", and " Never Let Me Down ".

Let n be the number of points and d the number of dimensions.

* Phone number, slang as digit, as in " Let me get your digits so I can call you tonight.

It is unclear which version of the paradox is stronger .< ref group =" Note "> Let be the number of civilizations ( per unit volume ) that can be seen at a radius.

Let be the number of particles at position at time.

Gloria Gaynor ( born September 7, 1949 ) is an American singer, best known for the disco era hits ; " I Will Survive " ( Hot 100 number 1, 1979 ), " Never Can Say Goodbye " ( Hot 100 number 9, 1974 ), " Let Me Know ( I Have a Right )" ( Hot 100 number 42, 1980 ) and " I Am What I Am " ( R & B number 82, 1983 ).

Let r be a non zero real number and let the r < sup > th </ sup > power mean ( M < sup > r </ sup > ) of a series of real variables ( a < sub > 1 </ sub >, a < sub > 2 </ sub >, a < sub > 3 </ sub >, ... ) be defined as

* Let be the least number such that there is a file with length bits that compresses to something shorter.

Let p be an odd prime number.

Let π ( x ) be the prime-counting function that gives the number of primes less than or equal to x, for any real number x.

Also, when The Beatles ' Let It Be was released in 1970, the magazine originally gave the album a poor review, yet in 2003, Rolling Stone ranked it number 86 in the magazine's list of the 500 Greatest Albums of All Time.

Let Q ( x ) denote the number of square-free ( quadratfrei ) integers between 1 and x.

LET x = rnd * 20! Let the value ' x ' equal a random number between ' 0 ' and ' 20 '

LET y = rnd * 20! Let the value ' y ' equal a random number between ' 0 ' and ' 20 '

Their first album, Let Them Eat Bingo, included the number one single " Dub Be Good to Me ", which caused a legal dispute revolving around allegations of infringement of copyright through the liberal use of unauthorised samples: the bassline was a note-for-note lift from " The Guns of Brixton " by The Clash and the lyrics borrowed heavily from " Just Be Good to Me " by The S. O. S.

Tone systems are certainly more complex than the number of units would suggest, and often analytically more difficult than much larger consonantal systems.

By applying this general principle, a great number of complex compounds of osmium, ruthenium, iridium, and rhenium, with triphenylphosphine, triphenylarsine, and triphenylstibine have been obtained in this laboratory during the past few years.

* Argument ( complex analysis ), a function which returns the polar angle of a complex number

It occupies a central place in modern mathematics and has multiple conceptual connections with such diverse fields as complex analysis, topology and number theory.

Alexander Grothendieck's work during the ` Golden Age ' period at IHÉS established several unifying themes in algebraic geometry, number theory, topology, category theory and complex analysis.

For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers.

This might sound complex, but first of all the number of di-atomic molecules that can exist at the temperatures of the atomizers used in AAS is relatively small, and second, the correction is performed by the computer within a few seconds.

In number theory, an arithmetic, arithmetical, or number-theoretic function is a real or complex valued function ƒ ( n ) defined on the set of natural numbers ( i. e. positive integers ) that " expresses some arithmetical property of n ."

Among the vast number of different biomolecules, many are complex and large molecules ( called biopolymers ), which are composed of similar repeating subunits ( called monomers ).

Particularly in team competition there can be a large number of bowls on the green towards the conclusion of the end, and this gives rise to complex tactics.

The inner product of two vectors is a complex number.

A more abstract definition, which is equivalent but more easily generalized to infinite-dimensional spaces, is to say that bras are linear functionals on kets, i. e. operators that input a ket and output a complex number.

( Technically, the quantum states are rays of vectors in the Hilbert space, as corresponds to the same state for any nonzero complex number c .)

On the left side, is a function mapping any point in space to a complex number ; on the right side, is a ket.

If A is a self-adjoint operator, then is always a real number ( not complex ).

* The Hermitian conjugate of a complex number is its complex conjugate.

for an arbitrary real or complex number α ( the order of the Bessel function ); the most common and important cases are for α an integer or half-integer.

where ν > − 1 / 2 and z is a complex number.

It differs from a retirement home, which is a single building or small complex, by having a number of autonomous households.

The number of ligands that react with a central metal atom can be found using the 18-electron rule, saying that the valence shells of a transition metal will collectively accommodate 18 electrons, whereas the symmetry of the resulting complex can be predicted with the crystal field theory and ligand field theory.

They are usually complex proprietary formulations containing Portland clinker and a number of other ingredients that may include limestone, hydrated lime, air entrainers, retarders, waterproofers and coloring agents.

and expresses the two parameters of the associated linear Cauchy distribution for x as a complex number:

* Complex conjugation, the involution multiplying the imaginary part of a complex number by − 1