Algebras Sentence Examples
All that can be done here is to give a sketch of the more important and independent special algebras at present known to exist.
Various special algebras (for example, quaternions) may be expressed in the notation of the algebra of matrices.
This applies also to quaternions, but not to extensive quantities, nor is it true for linear algebras in general.
The partitions being taken as denoting symmetric functions we have complete correspondence between the algebras of quantity and operation, and from any algebraic formula we can at once write down an operation formula.
Theoretically, no limit can be assigned to the number of possible algebras; the varieties actually known use, for the most part, the same signs of operation, and differ among themselves principally by their rules of multiplication.Advertisement
The algebras discussed up to this point may be considered as independent in the sense that each of them deals with a class of symbols of quantity more or less homogeneous, and a set of operations applying to them all.
In most cases these subsidiary algebras, as they may be called, are inseparable from the applications in which they are used; but in any attempt at a natural classification of algebra (at present a hopeless task), they would have to be taken into account.
In recent times many mathematicians have formulated other kinds of algebras, in which the operators do not obey the laws of ordinary algebra.
The geometrical interpretation of imaginary quantities had a far-reaching influence on the development of symbolic algebras.
Much of this work is based on the notion of a C* algebras, a natural abstraction of algebras of matrices.Advertisement
In Chapter 2. we give a short summary of parts of the theory of quantized enveloping algebras.
Another approach is to construct algebras directly from the algebraic group itself.
The method is similar in some respects to the treatment of non commutative algebras.
In the algebraic theory of data, continuous data types are modeled by topological algebras.
Since only finite regions are considered, the algebras are called local algebras.Advertisement
The importance of this algebra arises from the fact that in terms of such complex numbers with this definition of multiplication the utmost generality of expression, to the exclusion of exceptional cases, can be obtained for theorems which occur in analogous forms, but complicated with exceptional cases, in the algebras of real numbers and of signed real numbers.
When this fundamental truth had been fully grasped, mathematicians began to inquire whether algebras might not be discovered which obeyed laws different from those obtained by the generalization of arithmetic. The answer to this question has been so manifold as to be almost embarrassing.
The claim is that the allocation itself of observable algebras to finite space-time regions suffices to account for the physical meaning of observables.