# Square roots of matrix

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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(1)

for some scalar , then is called the eigenvalue of with corresponding eigenvector X.

There are several ways to construct X := squareroot of A . One way exploits the eigenvector-value factorization A = Q Q ^T =Q Q^TQ Q^T. =X^2,

Where X= Q Q^

=diag(squareroot of 1, squareroot of 2, squareroot of 3,.. squareroot of n)

where ...