Determine the dimension of the vector space W of the following n-square matrices: (a) symmetric matrices, (b) antisymmetric matrices, (d) diagonal matrices, (c) scalar matrices.
Added by Devon G.
Step 1
e., A = A^T. For an n x n symmetric matrix, the elements on the diagonal can be any real number, and the elements above the diagonal are equal to the corresponding elements below the diagonal. So, there are n diagonal elements and (n(n-1))/2 off-diagonal elements. Show more…
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