MATLAB: Scalar coefficients for a linear combination of matrices

linear combinationMATLABmatrices

Say I have the equation : aM + bN = C Where M, N and C are matrices and a, b are scalars. How do I find them knowing that C is a linear combination of M and N?

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HI Pierre-Luc

[M(:) N(:)]\C(:)   produces  [a;b]

This assumes that M and N are not proportional to each other, otherwise there are an infinite number of solutions.

Related Solutions

MATLAB: Linear Combination of 3 matrices.

There are an infinite number of linear combinations of matrices: you cannot compute them all.

Is it possible that the question you are dealing with has to do with finding the point that is at the intersection of linear combinations of three vectors?

MATLAB: Solve linear equation with added constant

Hello Gordon,

Since C is unknown, and a scalar, you could simply consider it to be an extension of the unknowns of x. So instead of x being an m-by-1 vector of unknowns, it's now an (m+1)-by-1 vector of unknowns, which still works since the system is overdetermined, as you said. So you can reformat your A matrix to have an added -1 to the end (for the coefficient to C), and simply solve the normal way:

[n, m] = size(A);
A_new = [A -ones(n, 1)];
x = A_new\B;
x_original = x(1:m);
C = x(end);

Hope that helps!

-Cam

Best Answer

Related Solutions

MATLAB: Linear Combination of 3 matrices.

MATLAB: Solve linear equation with added constant

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