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 the case of an object that is small compared with the radial distance to its axis of rotation, such as a tin can swinging from a long string or a planet orbiting in a circle around the Sun, the angular momentum can be expressed as its linear momentum,, crossed by its position from the origin, r. Thus, the angular momentum L of a particle with respect to some point of origin is

For example, in the Schrödinger picture, there is a linear operator U with the property that if an electron is in state right now, then in one minute it will be in the state, the same U for every possible.

For example, observable physical quantities are represented by self-adjoint operators, such as energy or momentum, whereas transformative processes are represented by unitary linear operators such as rotation or the progression of time.

For example, the condition number associated with the linear equation

For simplicity, the following descriptions focus on continuous-time and discrete-time linear systems.

For any n, the divergence is a linear operator, and it satisfies the " product rule "

For the statistics usage, see hierarchical linear modeling.

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

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 other ways to solve this kind of equations, see below, System of linear equations.

For example, according to ancient Hebrew belief, life takes a linear ( and not cyclical ) path ; the world began with God and is constantly headed toward God ’ s final goal for creation.

For an overview of a linear implementation of this framework, see linear regression.

For other examples of quotient objects, see quotient ring, quotient space ( linear algebra ), quotient space ( topology ), and quotient set.

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 molecules with N atoms in them, linear molecules have 3N – 5 degrees of vibrational modes, whereas nonlinear molecules have 3N – 6 degrees of vibrational modes ( also called vibrational degrees of freedom ).

For every finite dimensional matrix Lie algebra, there is a linear group ( matrix Lie group ) with this algebra as its Lie algebra.

For a population of size n, with a sequence of values y < sub > i </ sub >, i = 1 to n, that are indexed in non-decreasing order ( y < sub > i </ sub > ≤ y < sub > i + 1 </ sub >), the Lorenz curve is the continuous piecewise linear function connecting the points ( F < sub > i </ sub >, L < sub > i </ sub > ), i

For example, naive Bayes and linear discriminant analysis are joint probability models, whereas logistic regression is a conditional probability model.

For example, consider the case where the function is a linear function of the form

For example, bacterial chromosomes, plasmids, mitochondrial DNA and chloroplast DNA are usually circular double-stranded DNA molecules, while chromosomes of the eukaryotic nucleus are usually linear double-stranded DNA molecules.

For example, in classical mechanics, the derivative is used ubiquitously, and in quantum mechanics, observables are represented by linear operators.

For a time, urging Breasted to give up his public relations work and take up writing instead, he hoped to persuade him to become his assistant in research for the labor novel ; ;

For something, clearly, has gone very, very seriously wrong in Soviet-Chinese relations, which were never easy, and have now deteriorated.

For the interpretation of these significant investigations, it should be remembered that reciprocal relations exist in the hypothalamus with respect to autonomic and somatic functions which are closely associated with the emotions.

* For relations, see relation-preserving automorphism.

For two geometric objects P and Q represented by the relations P ( x, y ) and Q ( x, y ) the intersection is the collection of all points ( x, y ) which are in both relations.

For example, if, then,, and are three distinct relations.

For almost the next 1, 000 years, these states, their relations with each other, and their effects on the peoples who lived in stateless societies along their peripheries dominated Chad's political history.

For example, the Friends United Meeting and the Evangelical Friends International believe that sexual relations are condoned only in marriage, which they define to be between a man and a woman.

For Adorno and Horkheimer state intervention in the economy had effectively abolished the tension in capitalism between the " relations of production " and " material productive forces of society ," a tension which, according to traditional critical theory, constituted the primary contradiction within capitalism.

For example, all the relations are in third normal form and any relations with join and multi-valued dependencies are handled appropriately.

For example, Ecuador was more active in its relations with the Third World, multilateral organizations, Western Europe, and socialist countries.

: For more, see Micronesia-United States relations.

For a number of decades after WWII, the Federal Republic of Germany kept a notably low profile in international relations, because of both its recent history and its occupation by foreign powers.

For example, though most religions disapprove of extramarital sexual relations, it has always been widely practiced.

For monks and nuns, non-possession involves complete renunciation of property and human relations.

For the foreign relations of the current de facto Libyan government, see Foreign relations of Libya.

For instance, a TOE involving a set of different types of entities ( denoted by words, say ) and relations between them ( denoted by additional words ) is nothing but what mathematicians call a set-theoretical model, and one can generally find a formal system that it is a model of.

For Germany, because an autarkic economic approach or an alliance with Britain were impossible, closer relations with the Soviet Union to obtain raw materials became necessary, if not just for economic reasons alone.

For more information, see Cameroon-Nigeria relations.

For example, before the 2007 federal election, which Labor won, he criticised the then opposition industrial relations spokesperson Julia Gillard, saying she lacked an understanding of principles such as enterprise-bargaining set under his government in the late 1980s and early 1990s.

For a woman to have sexual relations when she is married to another ( which would include a situation such as polyandry ) would constitute adultery.