Manuals/calci/IDEMPOTENT

MATRIX("IDEMPOTENT",order)

• $order$ is the size of the Idempotent matrix.

Description

• This function is showing the idempotent matrix of order 3.
• An idempotent matrix is a matrix which, when multiplied by itself, is getting the same matrix.
• i.e.,A square matrix K is said to be idempotent if $K^{2}=K$.
• The properties of idempotent matrix is:

1. $K^{r}=K$ for r being a positive integer.
2. $I-K$ is idempotent.
3. If $K_{1}$ and $K_{2}$ are idempotent matrices and $K_{1}K_{2}=K_{2}K_{1}$. Then $K_{1}K_{2}$ is idempotent.

Examples

• 1.MATRIXTYPE("idempotent",IM(19)) = true
• 2.MATRIXTYPE([12,14],"idempotent") = false
• 3.MATRIXTYPE(IM(5)|*|2,"idempotent") = false

See Also

• IDENTITY
• SYMMETRIC
• PASCAL
• TRIANGULAR

References

• Idempotent matrix