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Square roots of matrix

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A) Let A be a positive definite matrix. Show that X has a unique positive square root. That is, show that there exists a unique positive matrix X such that X^2 =A.
B) How many square roots can a positive definite matrix have?

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Solution Summary

This is a proof regarding square roots of a positive definite matrix. How many square roots can a positive definite matrix have is determined.

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Problem:

A) Let A be a positive definite matrix. Show that X has a unique positive square root. That is, show that there exists a unique positive matrix X such that X^2 =A.
B) How many square roots can a positive definite matrix have?

Solution:
Definition: Let A be a linear transformation represented by a matrix . If there is a vector

such that ...

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