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Every vector a in three dimensions is a linear combination of the standard basis vectors i, j, and k.
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Every and vector
Every subset A of the vector space is contained within a smallest convex set ( called the convex hull of A ), namely the intersection of all convex sets containing A.
Every vector v in determines a linear map from R to taking 1 to v, which can be thought of as a Lie algebra homomorphism.
Every vector space has a basis, and all bases of a vector space have the same number of elements, called the dimension of the vector space.
Every normed vector space V sits as a dense subspace inside a Banach space ; this Banach space is essentially uniquely defined by V and is called the completion of V.
Every finite-dimensional vector space is isomorphic to its dual space, but this isomorphism relies on an arbitrary choice of isomorphism ( for example, via choosing a basis and then taking the isomorphism sending this basis to the corresponding dual basis ).
Every random vector gives rise to a probability measure on R < sup > n </ sup > with the Borel algebra as the underlying sigma-algebra.
Every continuous function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.
Every finite-dimensional Hausdorff topological vector space is reflexive, because J is bijective by linear algebra, and because there is a unique Hausdorff vector space topology on a finite dimensional vector space.
Every coalgebra, by ( vector space ) duality, gives rise to an algebra, but not in general the other way.
* Every holomorphic vector bundle on a projective variety is induced by a unique algebraic vector bundle.
For example, second-order arithmetic can express the principle " Every countable vector space has a basis " but it cannot express the principle " Every vector space has a basis ".
Many principles that imply the axiom of choice in their general form ( such as " Every vector space has a basis ") become provable in weak subsystems of second-order arithmetic when they are restricted.
Every vector space is free, and the free vector space on a set is a special case of a free module on a set.
Every and three
Every few minutes she would awaken for a moment to review things: Stowey, yes, was on his way south, and the two boys were away in school, and nothing was burning on the stove, and Lucretia was coming for dinner and bringing three guests of hers.
`` Every month, f'r three days '', he said happily, `` I take no water into my system, no water whatsoever.
Every week Holbrook writes the story line for the next three weeks for one of his strips and draws the next three weeks ' worth of strips for another.
* Every three years since Earnhardt's death, someone associated with Earnhardt has won the Daytona 500 ( his son Dale Earnhardt, Jr. in 2004, Earnhardt's replacement Cup driver Kevin Harvick in 2007, and Earnhardt Ganassi's Jamie McMurray in 2010.
Every January 19, in the early hours of the morning, the person made a toast of cognac to Poe's original grave marker and left three roses.
Every sequence can, thus, be read in three reading frames, each of which will produce a different amino acid sequence ( in the given example, Gly-Lys-Pro, Gly-Asn, or Glu-Thr, respectively ).
Good Trouble ( 1982 ) and Wheels Are Turnin ' ( 1984 ) were follow-up albums which also did well commercially, the former containing the hit singles " Keep the Fire Burnin '" ( U. S. # 7 ), " Sweet Time " ( U. S. # 26 ) and the un-ranked " The Key " and the latter containing the # 1 hit single " Can't Fight This Feeling " plus three more hits: " I Do ' Wanna Know " ( U. S. # 29 ), " One Lonely Night " ( U. S. # 19 ), " Live Every Moment " ( U. S. # 34 ) and the un-ranked " Break His Spell ".
Every game in the main Zelda series has consisted of three principal areas: an overworld in which movement is multidirectional, allowing the player some degree of freedom of action ; areas of interaction with other characters ( merely caves or hidden rooms in the first game, but expanding to entire towns and cities in subsequent games ) in which the player gains special items or advice ; and dungeons, areas of labyrinthine layout, usually underground, comprising a wide range of difficult enemies, bosses, and items.
From a pro-independence supporter's point of view, the movement for Taiwan independence began under Qing rule in the 1680s which led to a well known saying those days, " Every three years an uprising, every five years a rebellion ".
Every island has one or two short airstrips where Vanair ’ s Twin Otter planes land two or three times weekly.
Every three years, member nations that provide funds to the IDA gather together to replenish the IDA's resources.
However, the three propositions have different domains: the first proposition says something about " Every object ", while the second says something about " Every raven ".
Every third odd number is divisible by 3, which requires that no three successive odd numbers can be prime unless one of them is 3.
They draw three conclusions from Austin: ( 1 ) A performative utterance does not communicate information about an act second-hand — it is the act ; ( 2 ) Every aspect of language (" semantics, syntactics, or even phonematics ") functionally interacts with pragmatics ; ( 3 ) There is no distinction between language and speech.
Every night for three years, she undoes part of the shroud, until Melantho, one of twelve unfaithful serving women, discovers her chicanery and reveals it to the suitors.
In the autumn of 1970 Jurgen Wischnewski of the SPD declared, ‘ Every week more than three plans for reform come up for decision in cabinet and in the Assembly .’ ”
Every three months, it publishes a " Technology Quarterly ," a special section focusing on recent trends and developments in science and technology.
Every two years all eight districts of one of those groups elect all their three senators, assigning two of them from the party that obtains the majority, and one from the first minority party.
Every and dimensions
Every reality of the Marvel Universe has numerous interconnected dimensions, with each dimension differing from those of other realities ; for example, the Ultimate Asgard has clearly been shown to be distinct from the Asgard known to Earth-616 characters.
Every nontrivial proper rotation in 3 dimensions fixes a unique 1-dimensional linear subspace of R < sup > 3 </ sup > which is called the axis of rotation ( this is Euler's rotation theorem ).
Every year, the John the Baptist's feast day reveals the cosmic dimensions of this church: at the full midday of the summer solstice, when the sun is at its upper culmination over the earth, the light coming through the southern clerestorey windows create luminous spots that exactly locate in the full midst of the nave with a rigorous precision.
# Every Riemannian metric on a Riemann surface is Kähler, since the condition for ω to be closed is trivial in 2 ( real ) dimensions.
( Every Calabi – Yau manifold in 4 ( real ) dimensions is a hyperkähler manifold, because SU ( 2 ) is isomorphic to Sp ( 1 ).
Every rotation in three dimensions is defined by its axis — a direction that is left fixed by the rotation — and its angle — the amount of rotation about that axis ( Euler rotation theorem ).
Every plane B that is completely orthogonalTwo flat subspaces S < sub > 1 </ sub > and S < sub > 2 </ sub > of dimensions M and N of a Euclidean space S of at least M + N dimensions are called completely orthogonal if every line in S1 is orthogonal to every line in S2.
Chumbley considered the practice of willed dreaming essential as a means of interacting directly and consciously with the spiritual dimensions he called ' the High Sabbat '; according to him " Every word, deed and thought can empower, magnetise, and establish points of receptivity for a magical dream, likewise any of these means can do the opposite-fixating perception in a manner that is not receptive-that seals the soul in the body instead of enabling it to go forth at will.