Solve for A matrix in Ax = 0

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Mainak Dhar 2024-2-22

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评论： Mainak Dhar 2024-2-22

Hi,

I want to solve for a n x n matrix A when I know the n x 1 vector x and the system of linear equations is Ax = 0. The linear constraints I have on solving it is that each column should sum to 0 and I also know the diagonal elements of the A matrix. The matrix A is also tridiagonal, so the only non-zero elements are the ones on the main diagonal and the diagonals above and below it.

I can solve it by hand but unsure about how to do it using MATLAB. I assumed lsqlin would be able to do it but it seems like it only solves for the x vector.

Any ideas will be greatly appreciated. Thanks in advance.

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Torsten 2024-2-22

You have 2*n equations for 2*(n-1) degrees of freedom. So usually, your problem will not have a solution.

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采纳的回答

Matt J 2024-2-22

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https://ww2.mathworks.cn/matlabcentral/answers/2085523-solve-for-a-matrix-in-ax-0#answer_1414668

编辑：Matt J 2024-2-22

在 MATLAB Online 中打开

n=numel(x);
mask=tril(triu(ones(n),-1),+1);  %tridiagonal mask
A=optimvar('A',[n,n]);
prob = eqnproblem;
prob.Equations.eqn1=sum(A,1)==0;     %known column sums 
prob.Equations.eqn2=diag(A)==Adiag;  %known diagonal values
prob.Equations.eqn3=A.*mask==A;      %tridiagonal conition
prob.Equations.eqn4=A*x==0;          %A*x==0
[sol,fval,exitflag] = solve(prob);

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Matt J 2024-2-22

Yep, you're right.

Mainak Dhar 2024-2-22

Thanks all, for the explanations and the solutions. I'm sure I'm framing the question wrong but I can't figure out what. I believe I'll be able to solve it from here by putting in a little work. Much appreciated.

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