Trace T rA of a matrix A the sum of diagonal elements of a square matrix, e. g., T r(S) = x + y + z. Consider the space of zero trace symmetric matrices Sym0 = {S ∈ Sym|T r(S) = 0} Is the set Sym0 a subspace of Sym, Sym0 ⊂ Sym ? Expain. Find its basis and dimension dim Sym0

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