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Is it possible that a function take inputs as vectors in R^{n}and return one real value R. One such example is dot product. But keeping mathematical rigor in mind what should I call this function.

Problem 1.

Its a function from R^{2n}to R

or

a function such that f(R^{n},R^{n})->R

Problem 2.

I want to solve this equation using gradient descent

|c - x.y|

here

c - scalar (R)

x and y are vectors in Rn

How should I visualize its graph???

This problem is inspired by the mathematical treatment used to calculated SVD here.

As proved by Ecart and young there could only be one minimum of the equation and the minimum should be SVD. So it means it should be a sort of parabolloid. How to visualize it.

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# Function taking vectors of Rn as inputs

Can you offer guidance or do you also need help?

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