# How to compute distance with respect to inner product?

by Forextrader   Last Updated July 11, 2019 19:20 PM

Suppose $$A$$ is the invertible matrix:

$$A= \left[ {\begin{array}{cc} 2 & 0 & 1\\ 0 & 1 & -1\\ 1 & 0 & 1 \end{array} } \right]$$

We know that the function given by $$\langle\,u,v\rangle$$ = $$Au \cdot Av$$ is an inner product on $$R^3$$. Compute the distance between $$(1,0,0)$$ and $$(0,1,0)$$ with resepct to this inner product.

How would you go about solving this?

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