Arg min and arg max are sometimes also written argmin and argmax, and stand for argument of the minimum and argument of the maximum.

The Secretary of the Interior or any duly authorized representative shall be entitled to admission to, and to require reports from the operator of, any metal or nonmetallic mine which is in a State ( excluding any coal or lignite mine ), the products of which regularly enter commerce or the operations of which substantially affect commerce, for the purpose of gathering data and information necessary for the study authorized in the first section of this Act.

The second situation is illustrated by the operator T on Af ( F any field ) represented in the standard basis by Af.

The diagonalizable operator is the special case of this in which Af for each i.

( C ) if Af is the operator induced on Af by T, then the minimal polynomial for Af is Af.

If Af is the operator induced on Af by T, then evidently Af, because by definition Af is 0 on the subspace Af.

If Af are the projections associated with the primary decomposition of T, then each Af is a polynomial in T, and accordingly if a linear operator U commutes with T then U commutes with each of the Af, i.e., each subspace Af is invariant under U.

By Theorem 10, D is a diagonalizable operator which we shall call the diagonalizable part of T.

Then there is a diagonalizable operator D on V and a nilpotent operator N in V such that ( A ) Af, ( b ) Af.

The diagonalizable operator D and the nilpotent operator N are uniquely determined by ( A ) and ( B ) and each of them is a polynomial in T.

Since N and N' are both nilpotent and they commute, the operator Af is nilpotent ; ;

) Now Af is a diagonalizable operator which is also nilpotent.

Such an operator is obviously the zero operator ; ;

for since it is nilpotent, the minimal polynomial for this operator is of the form Af for some Af ; ;

but then since the operator is diagonalizable, the minimal polynomial cannot have a repeated root ; ;

hence Af and the minimal polynomial is simply x, which says the operator is 0.

If T is a linear operator on an arbitrary vector space and if there is a monic polynomial P such that Af, then parts ( A ) and ( B ) of Theorem 12 are valid for T with the proof which we gave.

This allows one to succinctly express, for example, the successor function as the addition operator partially applied to the natural number one.

In logic, a logical connective ( also called a logical operator or a truth function ) is a symbol or word used to connect two or more sentences ( of either a formal or a natural language ) in a grammatically valid way, such that the sense of the compound sentence produced depends only on the original sentences.

Objects were addressed using a syntax close to natural language, where objects were specified relative to the current card, or the operator was used to specify the absolute position of an object:.

There are also two natural gas-fired plants located at the Port of Morrow ; Coyote Springs I ( 255-276 MW ), owned and operated by Portland General Electric ; and Coyote Springs II ( 241-280 MW ; PGE operator ) owned by Avista Corp.

An enumeration operator is a set of pairs ( A, n ) where A is a ( code for a ) finite set of numbers and n is a single natural number.

* Transmission system operator, an entity involved in electric power transmission or transmission of natural gas

A fairly natural question to ask is whether there exists an operator, or half-derivative, such that

Simply using the Gamma function to remove the discrete nature of the factorial function ( recalling that, or equivalently ) gives us a natural candidate for fractional applications of the integral operator.

While working as a lathe operator and foreman at Midvale Steel, Taylor noticed the natural differences in productivity between workers, which were driven by various causes, including differences in talent, intelligence, or motivations.

It is more natural too, since it is simply the topology of pointwise convergence for an operator.

This is a natural rotationally invariant second-order differential operator.

Any bounded operator L that has finite rank is a compact operator ; indeed, the class of compact operators is a natural generalisation of the class of finite-rank operators in an infinite-dimensional setting.

where is the orthogonal projection onto K. This is a natural way to obtain an operator on K from an operator on the whole Hilbert space.

In computability theory, the μ operator, minimization operator, or unbounded search operator searches for the least natural number with a given property.

The mu operator " μy ", in either the unbounded or bounded form, is a " number theoretic function " defined from the natural numbers

Among the prisoners, Seaman First Class Joseph Randolph " Joe " Small, a winch operator in Division Four and a natural leader who called cadence when his division marched, was asked by officers to assemble a handful of reliable men as a team of acting petty officers and to keep the other prisoners on good behavior.

Fluxys () is a Belgium-based company, mainly acting as a natural gas operator.

Since a channel can be viewed as a linear operator, it is tempting to use the natural operator norm.

Put in another way, the kernel of a normal operator is the orthogonal complement of its range ; thus, the kernel of the operator coincides with that of for any.

If a normal operator on a finite-dimensional real or complex Hilbert space ( inner product space ) stabilizes a subspace, then it also stabilizes its orthogonal complement.

A complex number λ is said to be in the resolvent set, that is, the complement of the spectrum of a linear operator

Since subtracting 1 before complementing is equivalent to adding 1 afterwards, the operator would thus effectively add the ten's complement of the subtrahend.

* A semisimple operator ( or matrix ) is one for which every invariant subspace has an invariant complement.

In the case of a reflexive algebra of matrices with nonzero entries specified by a given pattern, the problem of finding the distance constant can be rephrased as a matrix-filling problem: if we fill the entries in the complement of the pattern with arbitrary entries, what choice of entries in the pattern gives the smallest operator norm?

* Set-theoretic union and intersection are dual under the set complement operator ⋅< sup > C </ sup >.

eMobile is a mobile virtual network operator MVNO which uses the Meteor Network for its services to residential & business customers, to complement the residential and business mobile services offered by Meteor.

Here, generalized regular expressions are defined like regular expressions, but they have a built-in complement operator.

a minterm is a logical expression of n variables that employs only the complement operator and the conjunction operator.

Moreover, the kernel of a closed densely defined operator T: H < sub > 1 </ sub > → H < sub > 2 </ sub > coincides with the orthogonal complement of the range of the adjoint.