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Linear Algebra Question 
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#1
Feb1612, 03:58 AM

P: 3

Let’s 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 


#2
Feb1712, 04:47 PM

Sci Advisor
P: 1,172

Just an idea:
Is the matrix A diagonalizable? If so, maybe the diagonal form would make it clearer . 


#3
Feb1712, 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.



#4
Feb1912, 06:07 AM

P: 3

Linear Algebra Question
i appreciate it. Thanx



#5
Feb1912, 06:16 AM

P: 3

How can I do that by using singular value decomposition?



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