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 polarization of light can be written as an equal combination of right-hand ( RHC ) and left-hand circularly ( LHC ) polarized light:

# 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 expression formed using any combination of the basic arithmetic operations and extraction of nth roots gives an algebraic number.

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

Any future Super Bowl that would have such a combination would have to have the Detroit Lions playing either the Cleveland Browns, Houston Texans, or Jacksonville Jaguars in the game.

* ` Class 2-Medium Rigid Vehicle ' - Any rigid vehicle with GLW less than 18, 001 kg ( with Light Trailer up to 3500 kg or less ), any combination vehicle with GCW less than 12, 001 kg, any rigid vehicle of any weight with no more than 2 axles, or any Class 1 vehicle.

* ' Class 3-Medium Combination Vehicle ' - Any combination vehicle of GCW less than 25, 001 kg or any Class 2 vehicle.

* ' Class 5-Heavy Combination Vehicle ' - Any combination vehicle of any weight, and any vehicle covered by previous classes.

Any word combination that corresponds to a complete subtree can be seen as a phrase.

Any word or any combination of words that are linked together by dependencies qualifies as a catena.

:" Any person who, on or in connection with any goods or services, or any container for goods, uses in commerce any word, term, name, symbol, or device, or any combination thereof, or any false designation of origin, false or misleading description of fact, or false or misleading representation of fact, which

Any combination of woods and charcoal may used.

Any data written to the database must be valid according to all defined rules, including but not limited to constraints, cascades, triggers, and any combination thereof.

Any material or combination can be used as mulch, stones, leaves, plastic, cardboard etc., though in Permaculture mulches of organic material are the most common because they perform more functions.

( a ) Any firearm which has a short stock and is designed to be held and fired by the use of a single hand ; and ( b ) Any combination of parts from which a firearm described in paragraph ( a ) can be assembled.

Any combination of meat or seafood can be used.

Any combination of the above symptoms can lead to severe panic attacks.

Any combination of outfielders, often three center fielders, could win the award in the same year.

* Any combination of multithreaded / SMT / CMP.

Any human face can be considered to be a combination of these standard faces.

Any combination of an electrolyte ( a fluid containing dissolved ions ) and insulating solid would generate electro-osmotic flow, though for water / silica the effect is particularly large.

Any variety or combination of meats, including chicken or turkey may be used to make jambalaya.

* AGSP ( Any Given Screen Position ) is the combination of VSP and Linecruncher, f. ex.