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 linear relations, regression analyses here are based on forms of the general linear model.

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 their purposes, oxygen and other gases were not drawn from the surrounding atmosphere through the medium of lungs but sustained artificially by solution in their shells.

For medium spans, trusses or box beams are usually most economical, while in some cases, the appearance of the bridge may be more important than its cost efficiency.

For example, the membrane around peroxisomes shields the rest of the cell from peroxides, and the cell membrane separates a cell from its surrounding medium.

For pre-recorded presentations, the rendered frames are transferred to a different format or medium such as film or digital video.

For example, one 640MB compact disc ( CD ) holds approximately one hour of uncompressed high fidelity music, less than 2 hours of music compressed losslessly, or 7 hours of music compressed in the MP3 format at a medium bit rate.

For waves that propagate in a medium, such as sound waves, the velocity of the observer and of the source are relative to the medium in which the waves are transmitted.

For waves which do not require a medium, such as light or gravity in general relativity, only the relative difference in velocity between the observer and the source needs to be considered.

For him, the unique essence of the cinema — that which could be duplicated in no other medium — is editing.

For light, the refractive index n, vacuum wavelength λ < sub > 0 </ sub >, and wavelength in the medium λ, are related by

For the gain medium to amplify light, it needs to be supplied with energy.

For continuous wave operation it is required for the population inversion of the gain medium to be continually replenished by a steady pump source.

For example, the average calfskin can provide three and half medium sheets of writing material.

( For example, in Europe a medium shot is framed from the waist up ).

For example, Escherichia coli may be exposed to UV radition, then plated onto agar medium.

For example, there could be a small partition, two medium partitions, and a large partition.

For nonlinear medium Gauss's law does not imply that the identity

For example, there are many common lasers ( e. g., dye lasers, carbon dioxide lasers ) where the laser medium consists of complete molecules, and energy states correspond to vibrational and rotational modes of oscillation of the molecules.

For example, the bread-and-butter Soldier class has medium armor, medium speed, and a well-rounded selection of weapons and grenades, while the Scout class is lightly armored, very fast, has a scanner that detects nearby enemies, but has very weak offensive weapons.

For example, in R-Type II, if the cannon is not fired when the ' BEAM ' bar has been charged completely, the gauge is able to enter a second stage of charging, and if the cannon is fired during this time, it launches a wide spread shot of medium power energy shots instead of a single large shot.

For example, the average calfskin can provide three and half medium sheets of writing material.

For electromagnetic waves the speed in a medium is governed by its refractive index according to

For example, based on the mechanical origin of acoustic waves, a moving disturbance in space – time can exist if and only if the medium involved is neither infinitely stiff nor infinitely pliable.

For waves on a string, or in medium such as water, the amplitude is a displacement.