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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