Idempotent matrix

[Abyt]

How to create idempotent matrix in sas/IML

[PeterClemmensen]

Any idempotent matrix?

[Abyt]

Thank you for your response. I need SAS/IML code to generate any idempotent matrix.

[PeterClemmensen]

Moved this thread to the IML Forum.

[SAS_Rob]

One way to generate an idempotent matrix is to use the formula:
M=I-(1/n)*ii`

where I is the identity matrix, n is the number of rows, and i is a column vector of 1s of dimension n.

This matrix is by definition orthogonal so that the rows are independent.  

I have included an example below of how this can be done in IML.

proc iml;
n=5;
i=j(n,1,1);
M=i(5)-((1/n)*i*i`);
m2=m*m;*check for idempotency;
print m m2;
quit;

[Rick_SAS]

To create a matrix in SAS/IML, use curly brackets to begin/end the matrix. Use spaces to separate columns and use commas to indicate a new row. For example:

proc iml;

A = { 1  0,
        0   1};

[Rick_SAS]

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