What is the non - commutative algebra (ep ≠ pe ) ?

Answer 1

DK

Answer 2

An operation is non-commutative if two elements operated with, like A X B where A and B are matrices, A x B is different from B x A. The matrix multiplication is defined on the property of the matrices i.e, row and column ordering. Whenever the operation defined uses the properties of the elements they are most likely to be non-commutative. These operations form a pivotal role in many areas of mathematics.

Answer 3

Non-commutative algebra is the study of the non-commutative rings and objects related to them. A non-commutative ring is a set over which you can do addition and multiplication, which has additive and multiplicative identities in it, both operations are associative and multiplication distributes over addition. However although addition operation has to be commutative, multiplication is not assumed to be so. A classical example is the ring of n x n matrices. For example if you take these two matrices
.....|1 0 |
A= |0 0|

and

.....| 0 0 |
B=| 1 0 |

Then AB=0 but BA=A =/= 0.

Answer 4

A non-commutative algebra is a set A with a binary operation * such that a*b is an element of A for all a and b in A. The non-commutative condition implies that not every pair (a,b), with a,b from A, satisfies a*b = b*a. (commutativity implies that a*b = b*a for all a,b in A) Matrix multiplication is a good example of non-commutativity.

An analogy of non-commutativity is putting on your shoes and socks. First you put your socks on, then your shoes - if you do it in the other order, you get a different result. I.e. order is important.

Answer 5

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Answer 6

it just means that if an operation is performed, on two numbers.. their sequence has to be considered. for eg.... 2 + 3 = 3 + 2. which is true. means this is commutative. however, in the case of matrices and determinants, this will NOT hold true. AxB will NOT be equal to BxA.

thats's non-commutative algebra.

Answer 7

commutative means that the result of A multiplying by B is the same as multiplying B by A.

non commutative means that this is not always the case.

You have this (non commutativity) with matrix multiplications : A*B is there not always the same as B*A

Answer 8

You haven't even defined an algebra. All you've said is that e*p not equal to p*e for some p and e (undefined) and some (undefined) binary operator * which is non-commutative.


Doug

Answer 9

commutative is e+p=p+e
associative is f(p+e)=p(f+e)