Matrix Entrywise Addition forms Abelian Group/Examples
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Examples of Matrix Entrywise Addition forms Abelian Group
$2 \times 2$ Matrices over Rational Numbers
Let $\Q^{2 \times 2}$ denote the set of order $2$ square matrices over the set $\Q$ of rational numbers.
Then the algebraic structure $\struct {\Q^{2 \times 2}, +}$, where $+$ denotes matrix entrywise addition, is an abelian group.
$n \times n$ Matrices over Real Numbers
Let $\R^{n \times n}$ denote the set of order $n$ square matrices over the set $\R$ of real numbers.
Then the algebraic structure $\struct {\R^{n \times n}, +}$, where $+$ denotes matrix entrywise addition, is an abelian group.