identity operator


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Noun1.identity operator - an operator that leaves unchanged the element on which it operates; "the identity under numerical multiplication is 1"
operator - (mathematics) a symbol or function representing a mathematical operation
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References in periodicals archive ?
Therefore, description of the measurement process should use orthogonal resolution of identity operator in a subspace determined by (3) or (5), not the identity operator in the whole [H.sub.q] [cross product] [H.sub.t].
[Z.sub.+] := {0, 1, 2, ...} is the set of nonnegative integers, [A.sup.0] := I, and I is the identity operator on X and
The identity operator [I.sub.H] is (most often) denoted as 1.
where I is an identity operator in [L.sup.2](h[Z.sup.m]).
where I is identity operator. The currents [J.sup.s.sub.l] and [M.sup.s.sub.l] generate the original scattering fields outside and zero field inside.
We show that the sequence [Q.sub.n] converges strongly to the identity operator by first showing that the sequence [[absolute value of ([Q.sub.n])].sub.1] is bounded.
If the sequence of positive linear operators does not converge to the identity operator then it might be useful to use some matrix summability methods (see e.g.
Here I[F] = F is the identity operator. Another set of equations is obtained with a tangential trace operator
As an operator on [L.sup.p], E is the projection onto the closure of range of T and E is the identity operator on [L.sup.p] if and only if [T.sup.-1][SIGMA] = [SIGMA].
Let I be the identity operator and [A.sub.i] be a sequence of bounded operators that commute with the mutually orthogonal projection operators [P.sub.i], then the operator 1 + [I.summation over (i=1)] [A.sub.i][P.sub.i] has a bounded inverse of the form 1 + [I.summation over (i=1)] [B.sub.i][B.sub.i], where [B.sub.i] = -[A.sub.i][(1 + [A.sub.i]).sup.-1].
If g = I, the identity operator, then problem (2.1) reduces to the following bifunction variational inequality problem of finding u [member of] K such that
we see immediately that the mapping [??]: [C.sup.[infinity]]([R.sup.2n+1]) [right arrow] [C.sup.[infinity]]([R.sup.2n+1]) is topological isomorphism from [C.sup.[infinity]]([R.sup.2n+1]) onto [C.sup.[infinity]]([R.sup.2n+1]) and [[??].sup.2] = I, where I is the identity operator of [C.sup.[infinity]]([R.sup.2n+1]).