Namely, the matrix is reduced to an upper triangular matrix by using elementary row operations, as in the first part of the Gaussian elimination method, taking care to preserve the sign of its determinant.

Namely, if A is the symmetric matrix that defines the quadratic form, and S is any invertible matrix such that D = SAS < sup > T </ sup > is diagonal, then the number of negative elements in the diagonal of D is always the same, for all such S ; and the same goes for the number of positive elements.

Namely, although eigenvalues attaining maximal absolute value may not be unique, the structure of maximal eigenvalues is under control: they have the form e < sup > i2πl / h </ sup > r, where h is some integer number — period of matrix, r is a real strictly positive eigenvalue, l = 0, 1, ..., h − 1.

Namely, a transsexual who has completed gender reassignment surgery is certainly not considered cross-dressing, unless they were to wear clothes of the gender opposite of what they have transitioned to.

Namely, the y-axis is necessarily the perpendicular to the x-axis through the point marked 0 on the x-axis.

Namely φ is universal for homomorphisms from G to an abelian group H: for any abelian group H and homomorphism of groups f: G → H there exists a unique homomorphism F: G < sup > ab </ sup > → H such that.

Namely, it is a " hostel " for hitchhikers, sized and specially designated to hold multiple hitchhikers at one time.

Namely, the unitary transformation that is the change of basis ( from the standard product basis into the Bell basis ) can also be implemented by quantum gates.

Let X be a topological vector space over K. Namely, X is a K vector space equipped with a topology so that vector addition and scalar multiplication are continuous.

Namely, it is necessary that these functions decrease sufficiently rapidly to zero ( in the neighborhood of infinity ) in order to insure the existence of the Fourier integral.

Namely, one considers the phase space of the corresponding classical system ( e. g. for an ensemble of quantum harmonic oscillators, the phase space of a classical harmonic oscillator is considered ).

It was not their Intention in the least at that Time to molest their Neighbours and Fellow Christians with Collections, for it has the appearance last Fall, as if they should have a promising Crop this Harvest, but that Hope is all lost for the most part of the Grane is kill'd with the Frost, and the Rest is destroy'd by the Insects, and now they have such a heavy Debt to pay, which they are not able to discharge out of their own Pokets: So they are obliged to implore all good-minded Christians who has it in their Hearts to promote the kingdom of Christ to assist them and lay some mite for the said Building of the said Church in the Hands of their Fellow Brothers wiiich they have send for that purpose Namely Albertus Simon and Jacob Weager.

Namely, Z is " If this sentence is true then Y ".

Namely, for any infinitesimal surface element C with normal direction and area dA, the circulation along the perimeter of C is the dot product where is the vorticity at the center of C.

Namely, libertarians believe that no person should have the right to decide for others what goods are necessary for living and which aren't, or that luxuries are necessarily wasteful, and thus argue that anti-consumerism is a precursor to central planning or a totalitarian society.

Namely, the question of how the interaction takes place, where in dualism ' the mind ' is assumed to be non physical and by definition outside of the realm of science.

Namely, the measures should be taken with positive and negative signs in such a way that the sum of the signs of for all parts that enclose a given point is 1 if belongs to, and 0 otherwise.

Namely, if a polynomial over with leading coefficient is reducible over then it is reducible over for any prime.

Namely, if is a smooth function, with and smooth manifolds, its derivative is a smooth function.

Namely, introducing the projectivization of the rank n complex vector bundle as the fiber bundle on B whose fiber at any point is the projective space of the fiber.

Namely, these are rotations by angles which are rational multiples of π.

Namely, the disco band Lipps Inc scored their only top 40 pop hit with their iconic song, " Funkytown ," originally penned by bandmember Steven Greenberg.

Namely the building, which was built by Szymon Piechowicz from Turobin, a chemist and a professor of medicine at the Zamość Academy, still houses a chemist's.

Namely, a pentacle refers to a pentagram circumscribed by a circle.

* Namely You — by Johnny Mercer & Gene de Paul ( 1956 ) Commander Publications

* The Maintenance of Free Trade, According to the Three Essentiall Parts of Traffique ; Namely Commodities, Moneys and Exchange of Moneys, by Bills of Exchanges for other Countries.

Namely, these churches were used by both Christian confessions existing in the region – Orthodox and Catholic.

He had three more hits in 1956 (" Wild Cherry ", " Ghost Town " and " Namely You "), all backed by orchestra leader Ray Conniff.

Gates stated that " the musical is cartoonish by definition and hardly one of Broadway's great treasures, but the show grows on you ", opining that " most of the Johnny Mercer – Gene de Paul songs are forgettable, but " Namely Me " ... stands out ".

Namely, Γ ( I ) is a subgroup of the group of norm 1 elements in the quaternion algebra generated as an associative algebra by the generators i, j and relations.

Namely, if the rock below the break is igneous or has lost its bedding by metamorphism, the plane of juncture is a nonconformity.

*: Now these are the nations which the L < SMALL > ORD </ SMALL > left, to prove Israel by them, even as many of Israel as had not known all the wars of Canaan ; 2: Only that the generations of the children of Israel might know, to teach them war, at the least such as before knew nothing thereof ; 3: Namely, five lords of the Philistines, and all the Canaanites, and the Sidonians, and the Hivites that dwelt in mount Lebanon, from mount Baal-hermon unto the entering in of Hamath.

Namely, these are rotations by angles which are rational multiples of π.

Namely, there exist topological manifolds which admit no C < sup > 1 </ sup >− structure, a result proved by, and later explained in the context of Donaldson's theorem ( compare Hilbert's fifth problem ).

Namely, Kuzmin proved the case where the exponent b is a real quadratic irrational, which was later extended to an arbitrary algebraic irrational b by Gelfond.

Namely, the ' cheeks ' on either side of the forward-facing fighter recovery bay which were inspired by the Smoke deflectors ( or lifters ) that appeared on some later steam locomotives.

Namely, the Centrifugal force created by the rotating section would essentially push the fighters out.

Namely, the legal rules and principles that: ( 1 ) define the authority and structure of administrative agencies ; ( 2 ) specify the procedural formalities employed by agencies ; ( 3 ) determine the validity of agency decisions ; and ( 4 ) define the role of reviewing courts and other governmental entities in relation to administrative agencies.

Namely, since behavioral intention cannot be the exclusive determinant of behavior where an individual's control over the behavior is incomplete, Ajzen introduced the theory of planned behavior by adding a new component, " perceived behavioral control.

Namely, within each PAN domain, communications will probably use short identifiers.

* There is a one-to-one correspondence between the two-sided ideals of M < sub > n </ sub >( R ) and the two-sided ideals of R. Namely, for each ideal I of R, the set of all n × n matrices with entries in I is an ideal of M < sub > n </ sub >( R ), and each ideal of M < sub > n </ sub >( R ) arises in this way.

Namely, these firms would have to literally insulate their banking and analysis departments from each other physically and with Chinese walls.

Namely, each affine form is stored as a list of pairs ( j ,), containing only the terms with non-zero coefficient.

Namely, a propositional formula can be expressed in first-order logic by replacing each propositional variable with a predicate of zero arity ( i. e., a predicate with no arguments ).