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st: RE: complex matrix

From   "FEIVESON, ALAN H. (AL) (JSC-SK) (NASA)" <[email protected]>
To   "'[email protected]'" <[email protected]>
Subject   st: RE: complex matrix
Date   Wed, 15 Oct 2003 14:10:09 -0500

Mitra - 

Suppose your original matrix is A + iB. Then by formal multiplication, you
can find matrices C and D such that (A + iB)*(C - iD) = I ....... provided
certain inverses exist.

Set the real part of the above product equal to I:

AC + BD = I

and set the imaginary part to zero:

BC - AD = 0

Solve these two equations for C and D. Then (C - iD) will be the inverse you
are looking for.
In order for this to work, you need A and W to be nonsingular where

W = A + B(A^-1)B

So if these inverses exist, Stata can calculate C and D for you.

Note: According to what I got, the solution is C = W^-1 and D = (A^-1)BC

where "X^-1" stands for "X-inverse"

Al Feiveson

-----Original Message-----
From: MITRA PINAKI (MAR1PXM) [mailto:[email protected]]
Sent: Wednesday, October 15, 2003 12:27 PM
To: [email protected]
Subject: st: complex matrix

Hello list,

   I'm wondering if Stata can calculate inverse and transpose of a complex
matrix. I have both real and imaginary parts in each cell of the complex

Thank you,

Pinaki Mitra

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