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

* 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 )

Using terms from formal language theory, the precise mathematical definition of this concept is as follows: Let S and T be two finite sets, called the source and target alphabets, respectively.

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 the line of symmetry intersect the parabola at point Q, and denote the focus as point F and its distance from point Q as f. Let the perpendicular to the line of symmetry, through the focus, intersect the parabola at a point T. Then ( 1 ) the distance from F to T is 2f, and ( 2 ) a tangent to the parabola at point T intersects the line of symmetry at a 45 ° angle.

Let us denote the time at which it is decided that the compromise occurred as T.

Let T be a linear operator represented by the matrix

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 T: X → X be a contraction mapping on X, i. e.: there is a nonnegative real number q < 1 such that

Let T be a set consisting of all infinite sequences of 0s and 1s.

Let K be a closed subset of a compact set T in R < sup > n </ sup > and let C < sub > K </ sub > be an open cover of K. Then

Let the curve be a unit speed curve and let t = u × T so that T, u, t form an orthonormal basis: the Darboux frame.

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 Af be the null space of Af.

Let N be a linear operator on the vector space V.

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??

Onkelos, a righteous convert and authoritative commentator of the same period, explained the verse, " Let Reuben live and not die ..." ( Deuteronomy 33: 6 ) to mean that Reuben should merit the World to Come directly, and not have to die again as result of being reincarnated.

John, one day, was going to bathe at Ephesus, and perceiving Cerinthus within, he then rushed out of the bath-house without bathing, exclaiming, " Let us fly, lest even the bath-house fall down, because Cerinthus, the enemy of the Truth, is within .” He wrote three epistles while living in Ephesus, and he also completed the Gospel of John during this period.

Let Freedom Ring began a period in which he performed with avant-garde jazz musicians rather than the veteran hard bop performers he had been playing with previously.

On March 17, 2005, Palmeiro appeared at a Congressional hearing about steroids in baseball and, while under oath, denied ever using steroids and stated, " Let me start by telling you this: I have never used steroids, period.

Let the memory of that period never pass from your mind ; Else you may be inclined to forget how merciful Providence has been in seizing us from such a people.

During this period, Peacock produced the album Barton Hollow by The Civil Wars and the song " O Love That Will Not Let Me Go " by Isaac and Anna Slade, and produced and performed on Jon Foreman's EPs Fall, Winter, Spring, and Summer.

Let be a piecewise continuously differentiable function which is periodic with some period.

Let Z < sub > n </ sub > denote the state in period n ( often interpreted as the size of generation n ), and let X < sub > n, i </ sub > be a random variable denoting the number of direct successors of member i in period n, where X < sub > n, i </ sub > are iid over all n ∈

During the duo's period of highest popularity, Tennille also worked as a session singer ( most frequently partnered with The Beach Boys ' Bruce Johnston ), performing as a backing vocalist on three Elton John albums including Caribou, Blue Moves, and 21 at 33 ( some vocally arranged by Dragon ) and most notably on the hit track " Don't Let the Sun Go Down on Me ".

Singles recorded during this period include " Let It Be Me ", " Who'll Stop The Rain " and " Different Drum ".

) Let a period be a temporary notation to establish grouping.

This period of decline and resignation from the world's cultural stage marked the rise of saudade, aptly described by a sentence of its national anthem —' Levantai hoje de novo o esplendor de Portugal ' ( Let us once again lift up the splendour of Portugal ).

He produced numerous short films and the three New Zealand feature films made in that period: Broken Barrier ( 1952 ) with Roger Mirams, Runaway ( 1964 ), and Don't Let It Get You ( 1966 ) for which he is most remembered.

Let us assume further that during the given period, 100 widgets were manufactured, using 212 kg of unobtainium which cost € 13, 144.

Let us assume further that during the given period, 100 widgets were manufactured, using 212 kg of unobtainium which cost € 13, 144.

Let us assume further that during given period, 100 widgets were manufactured, using 212 kg of unobtainium which cost € 13, 144.

Let be the total expenditure on good c in the base period, then ( by definition ) we have

Let be a periodic function of period 2π, which is continuous and has a continuous derivative throughout R, and such that

Another hit that emerged during this early period was 1973's " Let Me Be Your Lovemaker ", which peaked at number 55 on the Hot 100 and number 10 on the R & B chart, it was also the first instance ( after " Baby Sitter ") where Wright showed off her powerful whistle register vocals.

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

Smith's use of a dream sequence in Let Me Dream Again ( 1900 ), but is careful to note the precariousness of claiming any film the first to feature dream sequence given the rapid transnational development of cinema in its early years and that so many films from the period have been lost.

David Fricke of Rolling Stone has referred to this period as a " struggle " for Harrison " against the patronizing restrictions of writing within and for the Beatles ", while Doug Sulpy and Ray Schweighardt, authors of Get Back: The Unauthorized Chronicle of The Beatles ' Let It Be Disaster, observe that Harrison's songs were routinely rejected by Lennon and McCartney " even though some were far better than their own ".