For any positive definite matrix A, define the matrix B = log(A) by A = exp (B)

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For any positive definite matrix A, define the matrix B = log(A) by A = exp (B) = I + B + B2/2! + … + Br/r! + …

By inverting this series, or otherwise, show that log |A| = tr log (A), where ∣A∣ is the determinant of A.

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