Idempotent Element/Examples/Unit Matrix
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Example of Idempotent Element
Let $\mathbf I_n$ be the unit matrix of order $n$.
Then $\mathbf I_n$ is idempotent under the operation of (conventional) matrix multiplication.
Proof
From Unit Matrix is Identity for Matrix Multiplication, $\mathbf I_n$ forms an identity element for matrix multiplication.
The result follows from Identity Element is Idempotent.
$\blacksquare$
Sources
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): idempotent
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): idempotent