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My understanding of canonical form is very limited, and so may require some help.

Suppose a quadratic of the form:

$$ x_1*x_2+x_1*x_3=Q.$$

How would one go about putting that into canonical form, i.e. $$z_1^2+z_2^2+\cdots.$$

Many thanks.

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    Usually one uses rotations to remove cross-terms...2012-01-06
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    Ok, sorry to be naive, but how would you go about doing that? Many thanks.2012-01-06
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    If you've studied conic sections, you should have gone through the bit on [rotating coordinates](https://en.wikipedia.org/wiki/Cartesian_coordinate_system#Rotation); one can always pick an angle such that there is no cross term in the new coordinate system.2012-01-06
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    Do you mean by finding the eigenvalues of the characteristic matrix for the equation? If so, then this would not leave it in the required form unfortunately.2012-01-06

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