Linear Algebra Question


by mhdella
Tags: algebra, linear
mhdella
mhdella is offline
#1
Feb16-12, 03:58 AM
P: 3
Letís say that we have a constant matrix A which is the coefficients matrix and column vector U of control variable as well as column vector X of state variables:
X=A*U
The question is: What is the proper technique in Linear Algebra that I should do to know which element in U has the most impact on the corresponding perturbed element in X.
On other words, there is an element in X has been perturbed and I would like to correct it by adjusting a few (as less as I can) elements in U.
I know the maximum element in the corresponding row of A which is multiplied by U column vector would have the most effect and by that I will know the corresponding element in U, but I am searching about a formal linear algebra technique to deal with this not algorithmic or programming procedure
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Bacle2
Bacle2 is offline
#2
Feb17-12, 04:47 PM
Sci Advisor
P: 1,168
Just an idea:

Is the matrix A diagonalizable? If so, maybe the diagonal form would make it
clearer .
sunjin09
sunjin09 is offline
#3
Feb17-12, 07:30 PM
P: 312
If A is invertible, then the adjustment is unique, if A is rank deficient, the adjustment can be made minimal in L2 norm if you use pseudoinverse, if you want minimal L1 norm adjustment, you go with nonlinear optimization.

mhdella
mhdella is offline
#4
Feb19-12, 06:07 AM
P: 3

Linear Algebra Question


i appreciate it. Thanx
mhdella
mhdella is offline
#5
Feb19-12, 06:16 AM
P: 3
How can I do that by using singular value decomposition?


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