March 10th, 2010, 01:05 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, 05:12 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 is also matrix with vanish trace the subset W is a subspace. Its basis are the matrix units . The number of the linear independnt matrix units is n1. Hence . Each linear independant matrix can be basis of W.


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