01/22/2017, 10:29 PM
A few days ago, I post a question about the derivatives of these units. But to do it, I need to know everything about base units. I think this forum is optimal to collect our knowledges of it.
So a multidimensional number is from a linear combination of these units,
We multiply them like this way:
where i!=j,
is the levi-civita tensor which gives the sign of the multiplication, and ^ is a logic binary operator: xor.
And of course, we can represent them as matrices, too ... But just from reals to quaternions, because of the non-associativity of the octonions, the multiplication of the matrices of the representation of these octonions does not work ... I do not know why. (?)
I have many questions:
Why cannot we represent the octonions, sedenions ... etc.?
What is the derivative of
?
What is
(inverse)?
Which logic binary operators could we substitute instead of
?
What is the taylor series of the xor and the levi-civita ops?
How can we calculate with i[x] where x is not integer, so it is real or complex?
So a multidimensional number is from a linear combination of these units,
We multiply them like this way:
where i!=j,
And of course, we can represent them as matrices, too ... But just from reals to quaternions, because of the non-associativity of the octonions, the multiplication of the matrices of the representation of these octonions does not work ... I do not know why. (?)
I have many questions:
Why cannot we represent the octonions, sedenions ... etc.?
What is the derivative of
What is
Which logic binary operators could we substitute instead of
What is the taylor series of the xor and the levi-civita ops?
How can we calculate with i[x] where x is not integer, so it is real or complex?
Xorter Unizo
