ThmDex – An index of mathematical definitions, results, and conjectures.
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Definition D761
Identity matrix

Let $R$ be an D266: Identity ring such that
 (i) $0_R$ is an D270: Additive identity in $R$ (ii) $1_R$ is a D577: Multiplicative identity in $R$
A D102: Matrix $r : I \times J \to R$ is an identity matrix over $R$ if and only if
 (1) $$\forall \, i \in I : \forall \, j \in J \left( i \neq j \quad \implies \quad r_{i, j} = 0_R \right)$$ (2) $$\forall \, i \in I : \forall \, j \in J \left( i = j \quad \implies \quad r_{i, j} = 1_R \right)$$

Let $R$ be an D266: Identity ring such that
 (i) $0_R$ is an D270: Additive identity in $R$ (ii) $1_R$ is a D577: Multiplicative identity in $R$
A D2054: Diagonal matrix $r : I \times J \to R$ over $R$ is an identity matrix over $R$ if and only if $$\forall \, i \in I : \forall \, j \in J \left( i = j \quad \implies \quad r_{i, j} = 1_R \right)$$