Question

Being S(nxn) a subspace of the square matrix vector space. S is the subspace which contains all the symmetric matrix's. Prove that the dimension of S is:

dim S = [n*(n+1)/ 2]

Answer 1

If SUM (ARRAY) is specified, the result is the sum of all elements of ARRAY. If ARRAY has size zero, the result is zero.

If SUM (ARRAY, MASK=MASK) is specified, the result is the sum of all elements of ARRAY corresponding to true elements of MASK. If ARRAY has size zero, or every element of MASK has the value .FALSE., the result is zero.
The following rules apply if DIM is specified:

If ARRAY has rank one, the value is the same as SUM (ARRAY [,MASK=MASK]).

An array result has a rank that is one less than ARRAY, and shape (d1, d2, ..., dDIM-1, dDIM+1, ..., dn), where (d1, d2, ..., dn) is the shape of ARRAY.

The value of element (s1, s2, ..., sDIM-1, sDIM+1, ..., sn) of SUM (ARRAY, DIM [,MASK]) is equal to SUM (ARRAY (s1, s2, ..., sDIM-1, :, sDIM+1, ..., sn) [,MASK = MASK (s1, s2, ..., sDIM-1, :, sDIM+1, ..., sn)].

Answer 2

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