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 September 29th, 2008, 01:35 AM #1 Member   Joined: Dec 2007 Posts: 30 Thanks: 0 Matrix operations proof problem.. Help please.. I have some trouble with the following proof. Any help would be great! Let A be an n x n matrix. Show that A can be uniquely written A= X+Y, where X is symmetric (that is X^T=X) and Y is antisymmetric (that is, Y^T=-Y). [The usage Y^T represents the transpose of matrix Y) Thanks! September 29th, 2008, 02:34 AM #2 Site Founder   Joined: Nov 2006 From: France Posts: 824 Thanks: 7 Re: Matrix operations proof problem.. Help please.. Consider two coefficients a_ij and a_ji which are symmetric with respect to the principal diagonal of your matrix A=(a_mn). Your problem is equivalent with showing that there exists two numbers x_ij and y_ij such that: a_ij = x_ij + y_ij and a_ji = x_ji + y_ji = x_ij -y_ij. This system of equations has determinant -2 and thus admits a unique solution. This solves your problem. January 26th, 2009, 11:12 AM #3 Member   Joined: Jan 2009 Posts: 72 Thanks: 0 Re: Matrix operations proof problem.. Help please.. Let X=(A+A^T)/2 , Y=(A-A^T)/2 Tags matrix, operations, problem, proof 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 niaboc Algebra 1 October 2nd, 2012 11:51 AM questioner1 Linear Algebra 3 August 16th, 2012 08:03 AM Nexusfactor Linear Algebra 1 February 12th, 2012 02:16 AM CogitoErgoCogitoSum Algebra 1 January 11th, 2010 01:24 PM tmlfan_179027 Linear Algebra 3 October 3rd, 2009 12:43 AM

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