operator

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.

In the frame are two sets of bars which interact with each other to prevent the operator from making dangerous moves.

Here's how the scheme works: Suppose the operator pulls the lever to clear a particular signal.

Aging but still precocious, French feline enfant terrible Francoisette Lagoon has succeeded in shocking jaded old Paris again, this time with a sexy ballet scenario called The Lascivious Interlude, the story of a nymphomaniac trip-hammer operator who falls hopelessly in love with a middle-aged steam shovel.

The operator asked pityingly.

We are trying to study a linear operator T on the finite-dimensional space V, by decomposing T into a direct sum of operators which are in some sense elementary.

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.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

( 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.

Let us look at the operator Af.

When Af for each i, we shall have Af, because the operator Af will then be 0 on the range of Af.

Let N be a linear operator on the vector space V.

Let T be a linear operator on the finite-dimensional vector space V over the field F.

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 ; ;

( Actually, a nilpotent operator on an n-dimensional space must have its T power 0 ; ;

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

Such an operator is obviously the zero operator ; ;