# Identity matrix

From Encyclopedia of Mathematics

Revision as of 11:25, 2 April 2018 by Richard Pinch (talk | contribs) (also unit matrix, cite Aitken (1939))

*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 $M_n(R)$.

#### References

- A.C. Aitken, "Determinants and matrices", Oliver and Boyd (1939) Zbl 65.1111.05 Zbl 0022.10005

**How to Cite This Entry:**

Identity matrix.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Identity_matrix&oldid=43064