# 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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Hint: How would you usually calculate the distance between the two points? Can you formulate that in terms of the standard inner product? Now do the calculation with this new inner product instead of the standard one.

Arthur
July 11, 2019 19:17 PM

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