For each picture frame, the 6502 writes graphics commands for the DVG into a defined area of RAM ( the vector RAM ), and then asks the DVG to draw the corresponding vector image on the screen.

For example an absolute value is also defined for the complex numbers, the quaternions, ordered rings, fields and vector spaces.

For a vector with linear addressing, the element with index i is located at the address B + c · i, where B is a fixed base address and c a fixed constant, sometimes called the address increment or stride.

For an object with a fixed mass that is rotating about a fixed symmetry axis, the angular momentum is expressed as the product of the moment of inertia of the object and its angular velocity vector:

For any system, the following restrictions on measurement results apply, where is the reduced Planck constant and is any direction vector such as x, y, or z:

For a finite-dimensional vector space, using a fixed orthonormal basis, the inner product can be written as a matrix multiplication of a row vector with a column vector:

For a finite-dimensional vector space, the outer product can be understood as simple matrix multiplication:

For 2D vector animations, the rendering process is the key frame illustration process, while tweened frames are rendered as needed.

For example, binary string 1011 is represented by the vector ( 1, 0, 1, 1 ).

For the purposes of this article, we call this constructed vector the transmitted vector.

For a vector expressed in cylindrical coordinates as

For twisting rotation to exist, it is necessary to tilt the body sideways after takeoff, so that there is now a small component of this horizontal angular momentum vector along the body's long axis.

Malaria Foundation International states, " The outcome of the treaty is arguably better than the status quo going into the negotiations ... For the first time, there is now an insecticide which is restricted to vector control only, meaning that the selection of resistant mosquitoes will be slower than before.

For the special case, this implies that the length of a vector is preserved as well — this is just Parseval's theorem:

For a flow, the vector field Φ ( x ) is a linear function of the position in the phase space, that is,

For a more useful solution, we utilize vector identities, which work for any vector, as follows:

For example, an endomorphism of a vector space V is a linear map ƒ: V → V, and an endomorphism of a group G is a group homomorphism ƒ: G → G. In general, we can talk about endomorphisms in any category.

For any positive integer n, the set of all n-tuples of real numbers forms an n-dimensional vector space over R, which is denoted R < sup > n </ sup > and sometimes called real coordinate space.

For example, a bijective linear map is an isomorphism between vector spaces, and a bijective continuous function whose inverse is also continuous is an isomorphism between topological spaces, called a homeomorphism.

For example, upon rolling a 5-5 that player may move up to four separate checkers forward five spaces each.

For complete metric spaces this is equivalent to compactness.

For bassists with smaller hands, the large spaces between pitches may present a significant challenge, especially in the lowest range, where the spaces between notes are largest.

For example, if a child falls into a well and struggles to get out, he or she may develop a fear of wells, heights ( acrophobia ), enclosed spaces ( claustrophobia ), or water ( aquaphobia ).

For path-connected spaces, therefore, we can write π < sub > 1 </ sub >( X ) instead of π < sub > 1 </ sub >( X, x < sub > 0 </ sub >) without ambiguity whenever we care about the isomorphism class only.

For example, they are Hausdorff paracompact spaces ( and hence normal and Tychonoff ) and first-countable.

For measure spaces that are also topological spaces various compatibility conditions can be placed for the measure and the topology.

For a language like English, this is fairly trivial, since words are usually separated by spaces.

For locally compact spaces an integration theory is then recovered.

For natural lighting of interior spaces by admitting sunlight, see Daylighting.

For a given quadratic form, several different spaces of spinors with extra properties may exist.

For a brief period in fact, complete normed linear spaces where referred to as " Banach-Wiener " spaces in mathematical literature, based on terminology introduced by Wiener himself.

For instance, any isometry ( distance-preserving map ) between metric spaces is uniformly continuous.

For every vector space there exists a basis ( if one assumes the axiom of choice ), and all bases of a vector space have equal cardinality ( see dimension theorem for vector spaces ); as a result the dimension of a vector space is uniquely defined.

For example, algebraic topology makes use of Eilenberg – MacLane spaces which are spaces with prescribed homotopy groups.

For example, a topological group is just a group in the category of topological spaces.

For example, a corollary of the lemma is that normal T < sub > 1 </ sub > spaces are Tychonoff.

For over a hundred years Southerners have felt that the North was picking on them.

For the making of selections on the basis of excellence requires that any foundation making the selections shall have available the judgments of a corps of advisors whose judgments are known to be good: such judgments can be known to be good only by the records of those selected, by records made subsequent to their selection over considerable periods of time.

For some time this writer has been suggesting a Junior Judging Class for Intermediates over 16 and under 20 years of age who are ineligible to compete in the Junior Class.

`` For three days now a German reconnaissance plane has been over the city taking pictures.

For over the years he had received many such calls.

For this does not account for the integral, elemental power of that which grows with abounding vigor as the play unfolds, nor does it explain the strange numinous sense of presentness which comes over those who watch the play like a spell.

he would look right through you while you were talking to him, and if you said, `` For Christ's sake, Donald, you've got Prussian blue all over your shirt '', he would smile, and nod, and an hour later the paint would be all over his pants as well.

For this purpose he visited the Diet of Nuremberg in 1522, where he made the acquaintance of the Reformer Andreas Osiander, by whose influence Albert was won over to Protestantism.

For many years there was confusion amongst botanists over the generic names Amaryllis and Hippeastrum, one result of which is that the common name " amaryllis " is mainly used for cultivars of the genus Hippeastrum, widely sold in the winter months for their ability to bloom indoors.

For private suits the minimum jury size was 201 ( increased to 401 if a sum of over 1000 drachmas was at issue ), for public suits 501.

For example, those who drank over 3 units a day had nearly twice the risk of a hip fracture.

For the rest of the two spacecrafts ' pass over the near side of the Moon, Mattingly prepared to shift Casper to a circular orbit while Young and Duke prepared Orion for the descent to the lunar surface.

For example, the number of solutions of an equation over a finite field reflects the topological nature of its solutions over the complex numbers.

For simplicity, we shall here use the shorthand notation for representing the over operator.

Also, supporters of this view would characterize Luke ’ s portrayal of the Roman Empire as positive because they believe Luke “ glosses over negative aspects of the empire and presents imperial power positively .” For example, when Paul is before the council defending himself, Paul says that he is “ on trial concerning the hope of the resurrection of the dead ” ( Acts 23: 6 ).

For according to them, there were seven islands in that sea in their time, sacred to Persephone, and also three others of enormous size, one of which was sacred to Hades, another to Ammon, and another one between them to Poseidon, the extent of which was a thousand stadia ; and the inhabitants of it — they add — preserved the remembrance from their ancestors of the immeasurably large island of Atlantis which had really existed there and which for many ages had reigned over all islands in the Atlantic sea and which itself had like-wise been sacred to Poseidon.

For three hundred years, beginning with bishop Ansgar, the Hamburg-Bremen archbishopric had been designated as the " Mission of the North " and had jurisdiction over all missions in Scandinavia, North-Western Russia, Iceland and Greenland.

For example, the Barony of Grey of Codnor was in abeyance for over 490 years between 1496 and 1989, and the Barony of Hastings was similarly in abeyance for over 299 years from 1542 to 1841.

For comparison, the equator of the Sun requires just over 25 days for a complete rotation.

For every 100 females age 18 and over, there were 87. 4 males.

For every 100 females age 18 and over, there were 97. 5 males.