How to define a mapping from R^n to R

Hello everyone,

I am trying to define a mapping from R^n to R referred to as basis function in the picture attached.

I have to no idea how to proceed.

Any suggestions would be really helpful.

Thank you.

Answer 1

[Gowtham]

Hi Ajai,

I understand that you are given psi(y, u) in the space and want to map it to R space.

Assuming psi(y, u) is a column vector of size n, one way to map is by using dot product with a weight vector and performing sum on the result.

Example:

psi = [1; 2; 3];
weight = [2; 1; 2];
result = sum(weight .* psi);
result

result = 10

The above logic can be implemented in a function which maps . I hope it helps!

References:

• https://www.mathworks.com/help/symbolic/times.html
• https://www.mathworks.com/help/matlab/ref/sum.html