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Identity matrix

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unit matrix

A square matrix $I$ with entries $1$ on the main diagonal and $0$ otherwise: $$ I_{ij} = \delta_{ij} = \begin{cases} 1 & \text{if}\ i =j \\ 0 & \text{otherwise} \end{cases} $$ where $\delta$ is the Kronecker symbol.

If $R$ is a ring with identity and 0 and 1 are interpreted as elements of $R$, then $I$ is the identity element in the matrix ring $M_n(R)$.


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How to Cite This Entry:
Identity matrix. Encyclopedia of Mathematics. URL: http://www.encyclopediaofmath.org/index.php?title=Identity_matrix&oldid=43064