Hello, Alex.a777, you wrote: AA> Hello, kfmn, you wrote: K>> Hello, Alex.a777, you wrote: AA>>> Hello, kfmn, you wrote: K>>>> Hello, Alex.a777, you wrote: AA>>>>> you at n=2 will have a type equation: AA>>>>> A_1*X*A_1^T + A_2*X*A_2^T = B_1 + B_2, AA>>>>> where A_1, A_2, B_1, B_2, X - matrixes NxN AA>>>>> you it wanted to tell? K>>>> yes, all matrixes - dimensionalities NxN, and items in the total - a certain fixed amount which with N is not connected in any way, can be and 2. AA>>> 1) Well the method of the Gauss solves the equation of type AX=B. How plan it to apply to your system? I so understand, the iterative approach over a method of the decision of Slough? AA>>> 2) concerning a choice of methods, look https://www.mathworks.com/help/matlab/r … e_full.png K>> Probably, I insufficiently clearly expressed about the decision by means of extraction in a vector. I meant the following: If to paint system component-wise (in the scalar form) each of the equations will be linear concerning elements of a matrix X. I.e. if all columns of a matrix X to make in one long vector Y dimensionality N^2 we receive normal Slough of type CY=D, but with matrix N^2xN^2. And to solve it it is possible, but it would be desirable something faster. AA> here you to yourselves invented operation! Did not understand an initiating message, yes)) AA> I do not claim for an optimality, but there is an iterative approach: AA> 0) it is sampled X0 AA> 1) we solve Slough rather X_i+1: A_1*X_i+1 = [summ (B_i, i=1, n) - summ (A_i*X_i*A_i^T, i=2, n)] * (A_1^T) ^-1 AA> 2) while || X_i+1 - X_i ||> eps X_i = X_i+1 and on a step 1) Thanks for idea, but, at first, matrixes A_i can be not reversible, and secondly, whether such process will converge it the big question...