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On an exam, the question was asked wether any matrix A can be written as the sum of a matrix B and a antisymetric matrix C.

I answered yes because just take C as the zero matrix and thus A = A + 0. I believe this is correct since the definition of a antisymetric matrix

A = -AT

holds for a matrix filled with zeros. But I'm not enterely convinced if the zero matrix is not a special case that does not count.

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marked as duplicate by gimusi, Vladhagen, Namaste linear-algebra Sep 13 '18 at 0:10

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