Category:Definitions/Unit Matrices

This category contains definitions related to Unit Matrices.
Related results can be found in Category:Unit Matrices.

Let $R$ be a ring with unity whose zero is $0_R$ and whose unity is $1_R$.

Let $n \in \Z_{>0}$ be a (strictly) positive integer.

Let $\struct {\map {\MM_R} n, +, \times}$ be the ring of order $n$ square matrices over $R$.

Then the unit matrix (of order $n$) of $\struct {\map {\MM_R} n, +, \times}$ is defined as:

$\mathbf I_n := \sqbrk a_n: a_{i j} = \delta_{i j}$

where $\delta_{i j}$ is the Kronecker delta for $\map {\MM_R} n$.