Matrix/2305/Canonical decomposition/Exercise

We consider the matrix

${\begin{pmatrix}2&3\\0&5\end{pmatrix}},$

and the three decompositions

${}{\begin{pmatrix}2&3\\0&5\end{pmatrix}}={\begin{pmatrix}2&0\\0&5\end{pmatrix}}+{\begin{pmatrix}0&3\\0&0\end{pmatrix}}\,,$

${}{\begin{pmatrix}2&3\\0&5\end{pmatrix}}={\begin{pmatrix}2&3\\0&5\end{pmatrix}}+{\begin{pmatrix}0&0\\0&0\end{pmatrix}}\,$

and

${}{\begin{pmatrix}2&0\\0&5\end{pmatrix}}={\begin{pmatrix}2&0\\0&5\end{pmatrix}}+{\begin{pmatrix}0&0\\0&0\end{pmatrix}}\,.$

Which one is (or are) the canonical additive decomposition in the sense of fact (and with respect to which basis)?

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