First let me clarify this is not a homework question.
This part has cropped up as part of a small project i am doing on Cosmic microwave background.
How would i go about minimizing the function
f(x_{1},x_{2}...x_{n})=\Sigma*x_{i}*a_{i}
subject to the constraint:
\Sigma x_{i}*(2*i+1)=constant...
Everyone must be familiar with U(1),SU(2) and SU(3) Lie groups in particle physics .
But how does one define the multiplication of two groups of different dimensions
aka SU(2) X U(1) or SU(3) X SU(2) X U(1).