Difference between revisions of "Identity matrix"
From Encyclopedia of Mathematics
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A square matrix $I$ with entries $1$ on the main diagonal and $0$ otherwise: | A square matrix $I$ with entries $1$ on the main diagonal and $0$ otherwise: | ||
$$ | $$ | ||
| − | I_{ij} = \delta_{ij} | + | I_{ij} = \delta_{ij} = \begin{cases} 1 & \text{if}\ i =j \\ 0 & \text{otherwise} \end{cases} |
$$ | $$ | ||
where $\delta$ is the [[Kronecker symbol]]. | 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]] $M_n(R)$. | 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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| + | ====References==== | ||
| + | * A.C. Aitken, "Determinants and matrices", Oliver and Boyd (1939) {{ZBL|65.1111.05}} {{ZBL|0022.10005}} | ||
Latest revision as of 11:25, 2 April 2018
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=39112
Identity matrix. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Identity_matrix&oldid=39112