Consider an overdetermined system of linear equations, as might occur with repeated measurements of a physical phenomenon to compensate for experimental errors.

Consider the physical model of the citizenship of human beings in the early 21st century, where about 30 % are Indian and Chinese citizens, about 5 % are American citizens, about 1 % are French citizens, and so on.

Consider a 1D situation where there is a jump in the scalar conserved physical quantity, which is governed by the hyperbolic conservation law

Consider adopting a system of holidays in which time off is granted with an eye to minimum inconvenience to the operation of the plant.

Consider the tense system.

Consider a complete orthonormal system ( basis ),, for a Hilbert space H, with respect to the norm from an inner product.

Consider a state of the system, described by the single particle states ..., n < sub > N </ sub >.

Consider two observers O and O ', each using their own Cartesian coordinate system to measure space and time intervals.

Consider the system at the point it has reached equilibrium.

Consider a space ship traveling from Earth to the nearest star system outside of our solar system: a distance years away, at a speed ( i. e., 80 percent of the speed of light ).

Consider a system in which voters can vote for any candidate from any one of many parties ; suppose further that if a party gets 15 % of votes, then that party will win 15 % of the seats in the legislature.

Consider also the case of a vessel leaving a star system, or heading to the outer planets.

Consider a system are of localized, non-interacting absorbing centers.

Consider the continuous linear time-variant system

Consider the continuous linear time-invariant system

Consider an analogy to the previous example system.

Consider the simplest case, a system with one independent variable, time.

Consider the simple case of two-body system, where object A is moving towards another object B which is initially at rest ( in any particular frame of reference ).

Consider a system of K wire loops, each with one or several wire turns.

Consider a system of n linear equations for n unknowns, represented in matrix multiplication form as follows:

Consider a non-interacting fermion system ( a Fermi gas ), and suppose we " turn on " the interaction slowly.

Consider a system S and environment ( bath ) B, which are closed and can be treated quantum mechanically.

Consider a system of N qubits that is coupled to a bath symmetrically.

Consider a dynamical system of the form x < nowiki >'</ nowiki >

In times of war ( as seen in Consider Phlebas ), the Contact section of the Culture, and in particular Special Circumstances, acts as a military intelligence and special forces service.

In the case that T acts on euclidean space R < sup > n </ sup >, there is a simple geometric interpretation for the singular values: Consider the image by T of the unit sphere ; this is an ellipsoid, and its semi-axes are the singular values of T ( the figure provides an example in R < sup > 2 </ sup >).

Consider the problem of distributing objects given by a generating function into a set of n slots, where a permutation group G of degree n acts on the slots to create an equivalence relation of filled slot configurations, and asking about the generating function of the configurations by weight of the configurations with respect to this equivalence relation, where the weight of a configuration is the sum of the weights of the objects in the slots.

Consider first-order linear ODEs of the general form:

Consider a linear differential equation with constant coefficients

Consider an example of linear supply and demand curves.

Consider in a vector space V, the general linear group GL ( V ).

Consider a linear polymer to be a freely-jointed chain with N subunits, each of length, that occupy zero volume, so that no part of the chain excludes another from any location.

Consider the homogeneous linear ordinary differential

Consider a bounded linear transformation T defined everywhere over a general Banach space.

Consider the simple linear regression model

Consider a continuous linear operator A: H → H ( this is the same as a bounded operator ).

Consider the second-order homogeneous linear differential equation

Consider the linear differential equation with a constant w. Its exact basis solutions are and.

Consider the continuous linear time-variant system

Consider a linear differential operator with constant coefficients,

Consider the following system of linear equations in an FEA problem

Consider the second-order linear differential equation

Consider a linear model of the form

Consider a linear non-homogeneous ordinary differential equation of the form

Consider the following linear inhomogeneous differential equation:

Consider the linear subspace of the n-dimensional Euclidean space R < sup > n </ sup > that is spanned by a collection of linearly independent vectors