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 March 10th, 2010, 12:05 AM #1 Senior Member   Joined: Nov 2009 Posts: 129 Thanks: 0 basis and dimension The set of all nxn matrices having trace equal to zero is a subspace W of Mnxn. Find a basis for W. What is the dimension of W? The trace is: a11=+a22+a33+....+anxn=0
 March 10th, 2010, 04:12 AM #2 Newbie   Joined: Mar 2010 Posts: 4 Thanks: 0 Re: basis and dimension Since the sum of two matrix with vanished trace is also matrix with vanish trace and the product of matrix with vanish trace and the scalar $\lambda$is also matrix with vanish trace the subset W is a subspace. Its basis are the matrix units $E_{ij}$. The number of the linear independnt matrix units is n-1. Hence $\dim W= n-1$. Each linear independant matrix $(n-1)\times(n-1)$ can be basis of W.

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# find a basis n*n matrix trace with zero

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