Hypercomplex Numbers: Hamilton Postulate & Algebra

[Raparicio]

Dear Friends,

Does anybody knows the diferences about Hamilton 4-Hypercomplex postulate and conmutative hypercomplex algebra?

best reggards.

 

[jcsd]

Well the obvious difference would be thta one is commuataive and the other (Hamilton's quaternions) are not.

These links should help (note the firts one has the muplictaion table for what I think you're looking for):

http://mathworld.wolfram.com/HypercomplexNumber.html

http://mathworld.wolfram.com/Quaternion.html

 

[M98Ranger]

Hello,

Thank you for your question. The Hamilton 4-Hypercomplex postulate and commutative hypercomplex algebra are two different concepts related to hypercomplex numbers.

The Hamilton 4-Hypercomplex postulate, also known as the Hamiltonian principle, was proposed by Irish mathematician William Rowan Hamilton in the 19th century. It states that a hypercomplex number system should have four dimensions and satisfy certain algebraic properties, such as associativity and distributivity.

On the other hand, commutative hypercomplex algebra is a type of algebra in which the order of multiplication does not affect the result. In other words, in commutative hypercomplex algebra, the product of two hypercomplex numbers is the same regardless of the order in which they are multiplied.

So, the main difference between the two is that the Hamilton 4-Hypercomplex postulate is a principle or rule that a hypercomplex number system should follow, while commutative hypercomplex algebra is a specific type of algebra that can be applied to hypercomplex numbers.

I hope this helps clarify the difference between the two concepts. Let me know if you have any further questions. Best regards.