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Determine the square root of a matrix from infinite answers?

Posted 5 years ago

So, as I am sure many of you know, many matrices do not have unique square roots. Even something so simple as the 2x2 identity matrix has infinite results.

So, my question is: When a matrix is put into Mathematica, and we take the square root, does anyone know how Mathematica determines which of these infinite answers to use?

Or, better yet, in the interest of the Lagrangian in the theory I'm working with, it would be even better if I could force Mathematica to return the positive-definite result specifically. Does anyone know how one might go about this?

Any documentation or insight would be greatly appreciated. Thank you.

POSTED BY: L K
Posted 5 years ago

Presumably, the principal square root (see e.g. Higham) is being returned. If the matrices you are taking the root of are symmetric positive definite (since you mention the Lagrangian), the customary algorithms (surely being used by Mathematica under the hood) will definitely return SPD square roots.

POSTED BY: J. M.
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