inverse element

(redirected from Left invertible)

inverse element

[′in‚vərs ′el·ə·mənt]
(mathematics)
In a group G the inverse of an element g is the unique element g -1 such that g · g -1= g -1· g = e, where · denotes the group operation and e is the identity element.
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
References in periodicals archive ?
where the matrix A is left invertible, and B is the left inverse matrix of A, where [I.sub.n] is identity matrix.
In case of the right or left invertible plants with more inputs or outputs, respectively, we cannot divide the system into several separated SISO control loops.
System [summation] is left invertible if there exists a left inverse of [summation] in the sense of Definition 9.
If system (2) is left invertible, then it is possible to reconstruct uniquely the input u from the knowledge of the observed output sequence y.
[A.sub.1] - [lambda] is left invertible, [A.sub.2] - [lambda] is right invertible, [alpha]([A.sub.1] - [lambda]) = 0 = [beta]([A.sub.2] - [lambda]) and ind(A + K - [lambda]) = (ind([A.sub.1] - [lambda]) + ind([A.sub.2] - [lambda]) = 0 [??]) [beta]([A.sub.1] - [lambda]) = [alpha]([A.sub.2] - [lambda]).
The operators [T.sub.{a,b}] and [[??].sub.{a,b}] are invertible, only left invertible or only right invertible depending on whether the number x is equal to zero, positive or negative, respectively.
Due to the Vandermonde form of V(t), it is left invertible as long as K [greater than or equal to] L, so that [alpha] = [V.sup.[dagger]](t)y, where [V.sup.[dagger]] is the pseudoinverse of V.
So, for any invertible operator T [member of] B([M.supp.[perpendicular to]]), S [direct sum] T [member of] B(H) is a left invertible operator.
Consider a linear discrete--time, left invertible, strictly proper completely reachable and observable linear timeinvariant system described by the following equations:
It is clear that every coretraction (that is, a left invertible morphism) in [Pos.sub.S] is a regular monomorphism.
It means that all elements in [V.sub.0] are topologically left invertible. Since the element [x.sub.0] was chosen arbitrarily, the set [G.sup.t.sub.l](A) is open and the implication follows.