Difference between revisions of "Manuals/calci/IDEMPOTENT"

Latest revision as of 09:36, 15 May 2015

MATRIX("IDEMPOTENT",order)

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:

$K^{r}=K$ for r being a positive integer.
$I-K$ is idempotent.
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.

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-<div style="font-size:30px">'''IDEMPOTENT'''</div><br/>
+<div style="font-size:30px">'''MATRIX("IDEMPOTENT",order)'''</div><br/>
+*<math>order</math> 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 <math>K^2=K</math>.
+*The properties of idempotent matrix is:
+# <math>K^r=K</math> for r being a positive integer.
+# <math>I-K</math> is idempotent.
+# If <math>K_1</math>  and <math>K_2</math>  are idempotent matrices and <math>K_1K_2 =K_2K_1</math>. Then <math>K_1K_2</math> is idempotent.
+==Examples==
+*1.MATRIXTYPE("idempotent",IM(19)) = true
+*2.MATRIXTYPE([12,14],"idempotent") = false
+*3.MATRIXTYPE(IM(5)|*|2,"idempotent") = false
+==See Also==
+*[[Manuals/calci/IDENTITY| IDENTITY]]
+*[[Manuals/calci/SYMMETRIC| SYMMETRIC]]
+*[[Manuals/calci/PASCAL| PASCAL]]
+*[[Manuals/calci/TRIANGULAR| TRIANGULAR]]
+==References==
+*[http://en.wikipedia.org/wiki/Idempotent_matrix Idempotent matrix]