- #1
PoomjaiN
- 4
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Dear Friends & Colleagues,
I have a couple of nagging issues with mathematics I was hoping anyone of you would kindly be able to help resolve.
Given two vectors, x, y , I wish to define an operation ‘^’ such that x^y = x_1^y_1 + x_2^y_2 + ... .
For instance, if x_i designates the number of parameters of a model component of class i, and y_i designates the total number of model components of this class required, then x^y gives me the (Cartesian-product) dimension of my parametric search space. I referred to this ‘up-arrow’ operation as a sort of ‘pseudo-inner product’ in my Ph.D. thesis, which involved evolutionary optimisation over a combinatorial-parametric search space involving choices of model components and their resultant parametric specifications.
I wish to know (i) whether such a ‘pseudo-inner product’ had already been defined (if so, what is it called?), (ii) what kind of mathematical object would it be, and whether some kind of algebra can be defined on basis of its mapping? The construct may well extend to even though vis-à-vis my application I obviously had non-negative integers in mind.
Any enlightenment on this issue would be most truly appreciated.
Yours sincerely,
Poomjai Nacaskul (Ph.D.)
I have a couple of nagging issues with mathematics I was hoping anyone of you would kindly be able to help resolve.
Given two vectors, x, y , I wish to define an operation ‘^’ such that x^y = x_1^y_1 + x_2^y_2 + ... .
For instance, if x_i designates the number of parameters of a model component of class i, and y_i designates the total number of model components of this class required, then x^y gives me the (Cartesian-product) dimension of my parametric search space. I referred to this ‘up-arrow’ operation as a sort of ‘pseudo-inner product’ in my Ph.D. thesis, which involved evolutionary optimisation over a combinatorial-parametric search space involving choices of model components and their resultant parametric specifications.
I wish to know (i) whether such a ‘pseudo-inner product’ had already been defined (if so, what is it called?), (ii) what kind of mathematical object would it be, and whether some kind of algebra can be defined on basis of its mapping? The construct may well extend to even though vis-à-vis my application I obviously had non-negative integers in mind.
Any enlightenment on this issue would be most truly appreciated.
Yours sincerely,
Poomjai Nacaskul (Ph.D.)