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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? Tags definite, matrix, positive Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post edwardsharriman Linear Algebra 2 March 5th, 2016 11:19 PM whitegreen Linear Algebra 1 September 25th, 2015 05:41 AM zorroz Abstract Algebra 0 June 5th, 2012 12:14 PM Linear Algebra 2 January 19th, 2012 04:08 AM GaryG Math Software 0 July 7th, 2011 05:14 PM

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