Suppose G is positive definite. Show that (a) G is invertible and G1 is positive definite. (b)

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Suppose G is positive definite. Show that—

(a) G is invertible and G−1 is positive definite.

(b) G has a positive definite square root G1/2.

(c) G−1 has a positive definite square root G−1/2.

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