Find roots of quadratic matrix polyunomial

I'd like to solve the following equation where are square complex matrices.

Answer 1

[Malay Agarwal]

Hi @Andrea Baleani,

Please try the following code. This uses the fsolve function to solve the equation numerically.:

% Define the matrix A as a complex matrix
A = complex(randn(5,5), randn(5,5));

% Define the equation function handle
eq = @(X) A*X^2 + X + A;

% Define the initial guess for X
x0 = complex(randn(5, 5), randn(5, 5));

% Solve the equation for X using fsolve
X_solution = fsolve(eq, x0);

Solver stopped prematurely.

fsolve stopped because it exceeded the function evaluation limit,
options.MaxFunctionEvaluations = 2.500000e+03.

% Display the solution for X
disp('Solution for X:');

Solution for X:

disp(X_solution);

  10.4364 -14.8118i  -0.6416 -10.9103i   9.4393 + 6.4624i   0.8966 + 5.5707i  -1.4579 +11.0934i
  -6.2341 -22.7503i -18.8040 + 8.5239i  25.2421 -21.1322i -20.1716 + 8.5526i  -1.6253 + 6.1362i
  20.2211 - 1.4709i -21.2125 + 7.0483i  35.1446 + 2.8148i -45.9995 -20.6433i -21.7074 -13.8708i
  23.3683 - 2.0332i -13.0695 +15.8339i  30.7822 - 5.9025i -54.1409 - 4.7549i -30.4751 - 7.9421i
  -2.9071 -10.0220i  -1.5065 -36.7388i  -4.2081 +29.9107i  46.4775 -17.6436i  27.6587 + 6.8325i