Question 1164529
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<pre>

For any square matrix A,   


    A = {{{(1/2)*(A + A^t)}}} + {{{(1/2)*(A - A^t)}}}.     (1)


In this decomposition,  {{{A^t}}} is the matrix A "transposed".


In the decomposition (1), the matrix  B = {{{(1/2)*(A + A^t)}}}  is s symmetric matrix,  and  the matrix  C = {{{(1/2)*(A - A^t)}}}

is the skew-symmetric matrix.


So (1) provides a required decomposition.
</pre>

Solved.