My Math Forum Matrix - positive definite

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 January 16th, 2017, 07:07 AM #1 Senior Member   Joined: Feb 2015 From: london Posts: 121 Thanks: 0 Matrix - positive definite u is unit vector, i.e$\displaystyle ||u|| =1$, $\displaystyle u^Tu=1$ c is a positive constant M is a matrix I is the identity matrix $\displaystyle M = I + cuu^T$ In the first part of the question I had to calculate the matrix square root $\displaystyle M^{1/2}$ which has form $\displaystyle M^{1/2} = pI + quu^T$ From the answers I know that $\displaystyle p = \pm 1$ $\displaystyle 2pq + q^2 = c$ How can I prove that $\displaystyle M^{1/2}$ is *not* positive definte symmetric when p = -1? How can I prove that $\displaystyle M^{1/2}$ is positive definite symmetric when p = 1?

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