Post History
#2: Post edited
by
Derek Elkins
·
2021-02-09T00:42:01Z (almost 4 years ago)
This definitely isn't a number theory question. It's primarily about notation and generalized definitions. Abstract algebra seems the most appropriate and relevant field though the question arguably goes beyond it.
Why should a non-commutative operation even be called "multiplication"?
As per my knowledge and what was taught in school, >$a\times b$ is $a$ times $b$ or $b$ times $a$ Obviously this is commutative as $a$ times $b$ and $b$ times $a$ are same thing. On the other hand there are multiplications like **vector multiplication** and **matrix multiplication** that are not commutative. What does multiplication mean in general, for these? Or **should they even be called multiplication?**
#1: Initial revision
by
theabbie
·
2021-02-08T10:18:35Z (almost 4 years ago)
Why should a non-commutative operation even be called "multiplication"?
As per my knowledge and what was taught in school, >$a\times b$ is $a$ times $b$ or $b$ times $a$ Obviously this is commutative as $a$ times $b$ and $b$ times $a$ are same thing. On the other hand there are multiplications like **vector multiplication** and **matrix multiplication** that are not commutative. What does multiplication mean in general, for these? Or **should they even be called multiplication?**