Since-any-vector-v-is-a-linear-combination-∑-v-s

Since any vector v is a linear combination ∑ v j e j of its components, df is uniquely determined by df p ( e j ) for each j and each p ∈ U, which are just the partial derivatives of f on U. Thus df provides a way of encoding the partial derivatives of f. It can be decoded by noticing that the coordinates x 1 , x 2 ,... x n are themselves functions on U, and so define differential 1-forms dx 1 , dx 2 , ..., dx n .

Page "Differential form" ¶ 20

from Wikipedia

Promote Demote Fragment Fix

« More previous Okay Cancel More next »

Some Related Sentences

Since and any

Since more is known about Quiney than about any other acquaintance of Shakespeare in Stratford, his career may be followed to its sudden end in 1602.

Since she could not act, one part suited her as well as any other, and so she was the first person to offer Mr. Lincoln a glass of water, holding it up to the box, high above her head, to Miss Harris, who had asked for it.

Since accurate base maps are necessary for any planning program, the first step taken by the planning division to implement the long-range state plan has been to prepare two series of base maps -- one at a scale of 1 inch to a mile, and the second a series of 26 sheets at a scale of 1 inch to 2000 feet, covering the entire state.

Says NRLDA's James Wright: `` Since 1958 carriers that move material from the yard to the job site have undergone more radical changes than any of the dealer's other equipment ''.

Since Af is ferromagnetic, we felt that any results obtained from the magnetically contaminated Af would be suspect.

Since a Skeletal Age rating can be made at any age during growth, from Elbow, Shoulder, Knee, or Foot as well as Hand, it seems to be the method of choice when one wishes to study most aspects of skeletal developmental progress during childhood.

Since the psychiatric interview, like any other interview, depends on communication, it is significant to note that the therapist in this interview was a man of marked skill and long experience.

Since the 1946 disaster there have been 15 tsunami in the Pacific, but only one was of any consequence.

Since the widespread adoption of digital setting circles, any classical engraved setting circle is now specifically identified as an " analog setting circle " ( ASC ).

Since the time of Catherine II the ranks of Abbot and Archimandrite have been given as honorary titles in the Russian Church, and may be given to any monastic, even if he does not in fact serve as the superior of a monastery.

Since this holds true when performing addition on any real numbers, we say that " addition of real numbers is an associative operation.

Since this process does not involve any heat transfer or work, the First Law of Thermodynamics then implies that the net internal energy change of the system is zero.

Since the implementation of the Statute of Westminster 1931 in each of the Commonwealth realms ( on successive dates from 1931 onwards ), the Act of Settlement cannot be altered in any realm except by that realm's own parliament and, by convention, only with the consent of all the other realms, as it touches on the succession to the shared throne.

Since John Wesley ordained and sent forth every Methodist preacher in his day, who preached and baptized and ordained, and since every Methodist preacher who has ever been ordained as a Methodist was ordained in this direct " succession " from Wesley, then the Methodist Church teaches that it has all the direct merits coming from apostolic succession, if any such there be.

Since the New Testament never counters this instrumental language with any negative judgment on instruments, opposition to instruments instead comes from an interpretation of history.

Since the New Testament never condemns instruments themselves, much less in any of these settings, it is conceded that “ the church Fathers go beyond the New Testament in pronouncing a negative judgment on musical instruments .”

Since the runner would now have been at second anyway, the passed ball no longer has any impact on the earned / unearned calculation.

Since inside pitching is a legitimate tactic in baseball, courts have recognized that being hit by a pitch is an inherent risk of the game, so that players cannot sue for any resulting injuries.

" Since no one in the raiding party is carrying any change, nor do they realize that there is nothing stopping them from simply riding around the tollbooth, Taggart sends someone back to town to " get a shitload of dimes ".

Since the publication of Nineteen Eighty-Four the phrase " Big Brother " has come into common use to describe any prying or overly-controlling authority figure, and attempts by government to increase surveillance.

Since these are a basis, any quantum state of the particle can be expressed as a linear combination ( i. e., quantum superposition ) of these two states:

Since it is physically impossible for any Swedish town to face Jumne, the latter being situated along River Oder, Adam's statement is probably a misunderstanding.

Since the late nineteenth century, the South used a colloquial term, the one-drop rule, to classify as black a person of any known African ancestry.

Since the award criteria state that the Bronze Star Medal may be awarded to " any person ... while serving in any capacity in or with " the U. S. Armed Forces, awards to members of foreign armed services serving with the United States are permitted.

Since and vector

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since at a minimum the starting code address vector must always be valid on reset, systems commonly included some nonvolatile memory ( e. g. ROM ) starting at address zero to contain the vectors and bootstrap code.

Since the diagonal vector has a vertical component, the drive phase continues to provide some support against gravity and can be regarded as an extension of the support phase.

Since this construction works for any vector space V, we conclude that T is a functor from K-Vect to K-Alg.

Since the physicist's concept of force has a direction and a magnitude, it may be seen as a vector.

Since the typical vector operation would involve loading a small set of data into the vector registers and then running several operations on it, the vector system of the new design had its own separate pipeline.

Since this is an electromagnetic wave each electric field vector has a corresponding, but not illustrated, magnetic field vector that is at a right angle to the electric field vector and proportional in magnitude to it.

Since the propagation vector is proportional to the photon's momentum, the transverse propagation direction must remain the same in both regions.

Since the Poynting vector only occurs in Poynting's theorem as a divergence ∇ • S, the Poynting vector S is arbitrary to the extent that one can add a curl of a field F to S,

Since elements of W are necessarily elements of V, axioms 1, 2 and 5-8 of a vector space are satisfied.

Since then, the supercomputer market has focused much more on massively parallel processing rather than better implementations of vector processors.

Since a vector field is quite difficult to visualize at first, in elementary physics one may instead visualize this field with field lines.

Since the intensity or irradiance, I, of light is proportional to the square of the electric-field vector, the ellipticity becomes:

Since all these values are distinct, this is usually done using a bit vector.

However, the more difficult proof of the converse ( see below ) makes use of the vector space structure: Since both of the factors are vector spaces over Q, the tensor product can be taken over Q.

Since version 3. 0, Leveller includes vector shapes, which can be used for both modeling and coloration.

The set of ( p < sub > i </ sub >, n < sub > i </ sub >) is thus a sampling of a continuous vector ﬁeld V. The implicit function f is found by integrating the vector ﬁeld V. Since not every vector ﬁeld is the gradient of a function, the problem may or may not have a solution: the necessary and sufﬁcient condition for a smooth vector ﬁeld V to be the gradient of a function f is that the curl of V must be identically zero.

0.855 seconds.