Why the following statement is true? I am so frustrated that I could not have any clue on this problem.
The dimension of the vector space of all symmetric 4 by 4 matrices is 10.
Please help me.
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Try to write out a basis. You should have two types of elements in your basis: those with only nonzero entries on the diagonal (4 of them), and those with nonzero entries in only the $ij$th entry and the $ji$th entry, for $i<j$ (6 of them). – Jared May 21 '13 at 22:37
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A symmetric $\,n\times n\,$ matrix is completely characterized by the elements on its main diagonal and by those above it. How many elements are there...?
DonAntonio
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