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 ( m, n ) be a pair of amicable numbers with m < n, and write m = gM and n = gN where g is the greatest common divisor of m and n. If M and N are both coprime to g and square free then the pair ( m, n ) is said to be regular, otherwise it is called irregular or exotic.

Let denote the Bézier curve determined by the points P < sub > 0 </ sub >, P < sub > 1 </ sub >, ..., P < sub > n </ sub >.

Let P < sub > F </ sub > be the domain of a prefix-free universal computable function F. The constant Ω < sub > F </ sub > is then defined as

Let M be a smooth manifold and let x be a point in M. Let I < sub > x </ sub > be the ideal of all functions in C < sup >∞</ sup >( M ) vanishing at x, and let I < sub > x </ sub >< sup > 2 </ sup > be the set of functions of the form, where f < sub > i </ sub >, g < sub > i </ sub > ∈ I < sub > x </ sub >.

Let M be a smooth manifold and let f ∈ C < sup >∞</ sup >( M ) be a smooth function.

Let e be the error in b. Assuming that A is a square matrix, the error in the solution A < sup >− 1 </ sup > b is A < sup >− 1 </ sup > e.

Let us for simplicity take, then < math > 0 < c =- 2a </ math > and.

Let ( A < sub > i </ sub >)< sub > i ∈ I </ sub > be a family of groups and suppose we have a family of homomorphisms f < sub > ij </ sub >: A < sub > j </ sub > → A < sub > i </ sub > for all i ≤ j ( note the order ) with the following properties:

Let ( X < sub > i </ sub >, f < sub > ij </ sub >) be an inverse system of objects and morphisms in a category C ( same definition as above ).

* Let the index set I of an inverse system ( X < sub > i </ sub >, f < sub > ij </ sub >) have a greatest element m. Then the natural projection π < sub > m </ sub >: X → X < sub > m </ sub > is an isomorphism.

Let A = ( a < sub > ij </ sub >) be an n × n positive matrix: a < sub > ij </ sub > > 0 for 1 ≤ i, j ≤ n. Then the following statements hold.

Let x < sub > i </ sub > denote the concentration of strain i ; let a < sub > i </ sub > denote the rate at which strain i reproduces ; and let Q < sub > ij </ sub > denote the probability of a virus of strain i mutating to strain j.

Genesis 1: 9 " And God said, Let the waters be collected ". Letters in black, < font color ="# CC0000 "> niqqud in red </ font >, < font color ="# 0000CC "> cantillation in blue </ font >

* Let D < sub > 1 </ sub > and D < sub > 2 </ sub > be directed sets.

* Let R :=

Let φ: M × R → M be the one-parameter semigroup of local diffeomorphisms of M induced by the vector flow of Y and denote φ < sub > t </ sub >( p ) := φ ( p, t ).

Let A :=

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.

Let be a set with a binary operation ( i. e., a magma ).

Let G be a group with identity element e, N a normal subgroup of G ( i. e., N ◁ G ) and H a subgroup of G. The following statements are equivalent:

Let A be an m by n matrix ( i. e., A has m rows and n columns ).

Let us consider two patterns made of parallel and equidistant lines, e. g., vertical lines.

Let be an interval of real numbers ( i. e. a non-empty connected subset of ).

Let K be a number field ( i. e., a finite extension of ), in other words, for some by the primitive element theorem.

Let T be the period ( for example the time between two greatest eastern elongations ), ω be the relative angular velocity, ω < sub > e </ sub > Earth's angular velocity and ω < sub > p </ sub > the planet's angular velocity.

and switches between b-1 and b bits for Golomb code ( i. e. M is not a power of 2 ): Let.

Let ℓ ( e ) be the length of the edge e and θ ( e ) be the dihedral angle between the two faces meeting at e, measured in radians.

Let e be an index of the composition, which is a total computable function.

Let M be a monoid with identity element e and let A be the set of all subsets of M. For two such subsets S and T, let S + T be the union of S and T and set ST =

Both Kember and Pierce continue to perform some Spacemen 3 songs live ( e. g. " Transparent Radiation ", " Revolution ", " Suicide ", " Set Me Free ", " Che " and " Let Me Down Gently " ; and " Walkin ' with Jesus ", " Amen " and " Lord Can You Hear Me?

Many episode titles parodied the titles of Bond films, e. g. “ Live and Let ’ s Dance .”

Let K be a field, and let A be a vector space over K equipped with an additional binary operation from A × A to A, denoted here by · ( i. e. if x and y are any two elements of A, x · y is the product of x and y ).

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.