Multiplication of a rotated vector entries

[baggiano]

Hello

Is there any known operation/notation to express the multiplication of the entries of a rotated vector? More precisely, is there an alternative expression to replace the product operator for the following expression:
$$\prod_i^3(RP)_i$$
where R is the rotation matrix and P a vector in R^3.

Thanks in advance for any idea you might have.

Bag

 

[Stephen Tashi]

If R is rotation about an axis by angle through the origin by angle $$\theta$$ then a product of 3 R's rotates by angle $$3 \theta$$ and the product of the R's is a rotation matrix for than angle. It that what you're asking?

 

[baggiano]

Hi Stephen

Actually what is meant is the following: the rotation matrix R multiplied by the vector P returns the rotated vector P'. Then, the product operator $$\prod$$ gives me a scalar by multiplying the 3 entries of the vector P'. I was wondering if the last product operation could somehow be described using some other kinds of operators/operations (like for instance a projection). Sorry, the question can look a little naive but the fact that I need to multiply the entries of P' is not very convenient for me as it is difficult to treat.

Thanks for the reply anyway.

Bag