Any-linear-polarization-of-light-can-be-written-as

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Any and linear

Any field may be used as the scalars for a vector space, which is the standard general context for linear algebra.

:“ Any linear map from V to an algebra A can be uniquely extended to an algebra homomorphism from T ( V ) to A .”

Any linear combination of the column vectors of a matrix A can be written as the product of A with a column vector:

# Any sequence satisfying the recurrence relation can be written uniquely as a linear combination of solutions constructed in part 1 as λ varies over all distinct roots of p ( t ).

Any linear functional α on tangent vectors can be expanded in terms of the dual basis θ

* Any linear functional L is either trivial ( equal to 0 everywhere ) or surjective onto the scalar field.

Any two meromorphic 1-forms will yield linearly equivalent divisors, so the canonical divisor is uniquely determined up to linear equivalence ( hence " the " canonical divisor ).

* Any linear function is both concave and convex.

A weight on a Lie algebra g over a field F is a linear map λ: g → F with λ ( y )= 0 for all x, y in g. Any weight on a Lie algebra g vanishes on the derived algebra and hence descends to a weight on the abelian Lie algebra g /.

Any smooth function of one variable approximates a quadratic function when examined near enough to its minimum point ; and therefore the force — which is the derivative of energy with respect to displacement — will approximate a linear function.

: Any linear transformation f: V → A from V to an algebra A over K can be uniquely extended to an algebra homomorphism from T ( V ) to A as indicated by the following commutative diagram:

Any anisotropic or isotropic linear algebraic group over a field becomes split over the algebraic closure, so this distinction is interesting from the point of view of Algebraic number theory.

Any linear order can be bent into a circle, and any cyclic order can be cut at a point, resulting in a line.

Any point that is rigidly connected to the body can be used as reference point ( origin of coordinate system L ) to describe the linear motion of the body ( the linear position, velocity and acceleration vectors depend on the choice ).

* Any linear operator between two finite-dimensional normed spaces is bounded, and such an operator may be viewed as multiplication by some fixed matrix.

Any linear code can be represented as a graph, where there are two sets of nodes-a set representing the transmitted bits and another set representing the constraints that the transmitted bits have to satisfy.

Any linear time-invariant operation on s ( t ) produces a new spectrum of the form H ( f )• S ( f ), which changes the relative magnitudes and / or angles ( phase ) of the non-zero values of S ( f ).

Any system in a large class known as linear, time-invariant ( LTI ) is completely characterized by its impulse response.

Any linear function is homogeneous of degree 1, since by the definition of linearity

Any linear combination

Any other sequence satisfying this recurrence relation can be represented as a linear combination of the Lucas sequences U < sub > n </ sub >( P, Q ) and V < sub > n </ sub >( P, Q ).

Any linear system containing only voltage sources, current sources, and other resistors can be converted to a Thévenin equivalent circuit, comprising exactly one voltage source and one resistor representing " internal resistance ".

Any Jacobi field can be represented in a unique way as a sum, where is a linear combination of trivial Jacobi fields and is orthogonal to, for all.

Any and polarization

Any dielectric material develops a dielectric polarization ( electrostatics ) when an electric field is applied, but a substance which has such a natural charge separation even in the absence of a field is called a polar material.

Any ( fixed ) polarization can be described in terms of the shape of the polarization ellipse, which is defined by two parameters: axial ratio AR and tilt angle.

Any and light

Any information may be conveyed by an analog signal ; often such a signal is a measured response to changes in physical phenomena, such as sound, light, temperature, position, or pressure.

Conclusion: Any light beam moving vertically downwards in the concavity of the parabola ( parallel to the axis of symmetry ) will bounce off the parabola moving directly towards the focus.

Any combination of four things might happen with this light ray: absorption, reflection, refraction and fluorescence.

* ' Class 4-Heavy Rigid Vehicle ' - Any rigid vehicle of any weight, any Combination vehicle which consists of a heavy vehicle and a light trailer, or any vehicle of Class 1 or 2 ( but not 3 ).

Any light entering the hole is reflected indefinitely or absorbed inside and is unlikely to re-emerge, making the hole a nearly perfect absorber.

Any energy released by the explosion not radiated away in the burst itself takes the form of matter or energy moving outward at nearly the speed of light.

Any rivalry between Menahem and Pekah could only appear more and more foolish in light of the growing menace of Assyria.

Any instrument will reach a point where an increase in sample concentration will not result in an increase in the reported absorbance, because the detector is simply responding to the stray light.

Any tint further reduces incoming light to the retina, and yellow tints also reduce glare-recovery times for night drivers.

Any habitual pattern which is interrupted unexpectedly will cause sudden and light trance.

Any more-or-less arbitrarily chosen system of axioms is the basis of some mathematical theory, but such an arbitrary axiomatic system will not necessarily be free of contradictions, and even if it is, it is not likely to shed light on anything.

Any intense exposure to UV light can lead to photokeratitis.

Any possible course of experience resulting from a possible course of action will apparently underdetermine our surroundings: it would determine, for example, that there is either white wallpaper under red light or red wallpaper under white light, and so on.

Any noise introduced by the light source or the optical system will deteriorate the detectability of the technique.

Any light that is outside the short coherence length will not interfere.

Any light produced in the core of a star will interact with gas particles in the outer layers of the star, making it impossible to observe the core directly.

Any drift ( change in the light source ) between measurements will introduce errors.

Any media that allows some light to pass through typically works as a master.

Any bright flash of light would turn him back into Bruce Gordon.

Any light shade of diamond other than Light Yellow or Light Brown automatically falls out of the scale.

: Any ray of light moves in the " stationary " system of co-ordinates with the determined velocity c, whether the ray be emitted by a stationary or by a moving body.

Any fully polarized, partially polarized, or unpolarized state of light can be represented by a Stokes vector ().

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