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AB = kB*A

17 Apr 2008 (Updated 17 Jun 2009)

Solves the homogeneous linear system A*B = k*B*A

File Information
Description	An interesting homework assignment is to solve the homogeneous linear matrix system, AB = kB*A. This is a form of a linear algebraic Riccati equation. When k = 1, this always has a solution for real A. When k = -1, the solution only exists for specific matrices A. abba uses a kron trick to reformulate this as a standard linear system, then solves the problem for one specific (arbitrary) solution.
MATLAB release	MATLAB 7.4 (R2007a)
Zip File Content
Other Files	abba.m, license.txt

Tags for This File
Everyone's Tags	homogeneous(2), linear(2), linear algebra, riccati, system
Tags I've Applied
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Comments and Ratings (5)
21 Apr 2008	John D'Errico	I've updated a new release already - improving the help. Make sure you download the update.
22 Apr 2008	Marco Pittaluga	in the title there is AB=kBA and after there is Ab=kBA... now... question is: AB or Ab? Is different
25 Apr 2008	Kacem Baraket	do not tell the applications in engineering of this equation
15 Jun 2009	Bruno Luong	A small bug at line 70. It should be (transpose, not conjugate transpose in the second kron) M = kron(eye(n),A) - kron(k*A.',eye(n))
17 Jun 2009	Laoji Zhou

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Updates
21 Apr 2008	Improved the help
23 Apr 2008	A one character change in the summary: b --> B
17 Jun 2009	Removed the requirement for real inputs, also fixed the problem with transpose versus ctranspose as pointed out by Bruno.

Tag Activity for this File
Tag	Applied By	Date/Time
linear algebra	John D'Errico	22 Oct 2008 09:58:08
homogeneous	John D'Errico	22 Oct 2008 09:58:08
linear	John D'Errico	22 Oct 2008 09:58:08
riccati	John D'Errico	22 Oct 2008 09:58:08
system	John D'Errico	22 Oct 2008 09:58:08
linear	loganathan r	09 Jul 2009 00:59:39
homogeneous	loganathan r	09 Jul 2009 00:59:47

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