Why do my laptop and work computer produce different results when adding a small term to a matrix?

In the following code, when I add the term eye(8)*(0.0001) to the matrix F, my laptop and my work computer return different values for the variable Uk. Could anyone please help me understand what is happening?

I am using MATLAB R2024a on both computers.

clear; clc;

% constants
a = 1;
x1 = 1;
x2 = 0;
x4 = 0;
lambda = 1;

sigma3 = diag([1 1 1 1 -1 -1 -1 -1]);

kx = -2.0944;
ky = -3.6276;

F = [ – 0.4444*x4*lambda^3 + (2.0*x1 + 2.0*x2)*lambda, – lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.3333 – 4.082e-17i) – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.8889 + 5.551e-17i) + exp(a*kx*0.5i)*(0.8889 + 5.551e-17i)) + x4*lambda^3*(exp(-a*kx*0.5i)*(0.8889 + 1.11e-16i) + exp(a*kx*0.5i)*(0.8889 + 1.11e-16i)) + x4*lambda^3*(exp(-a*kx*0.5i)*(0.2222 – 2.721e-17i) + exp(a*kx*0.5i)*(0.2222 – 2.721e-17i)), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.7778 – 1.347i), lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.1111 + 0.1925i), 0, lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.6667 – 8.164e-17i) + x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*1.54i – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.4444 – 5.443e-17i) + exp(a*kx*0.5i)*(0.4444 – 5.443e-17i)), – lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.3333 – 0.5774i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.6667 + 0.3849i) + x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i)*(0.8889 + 1.11e-16i) + exp(a*kx*0.25i – a*ky*0.433i)*(0.8889 + 1.11e-16i)), – lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.3333 + 0.5774i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.2222 – 1.155i) – 1.0*x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i)*(0.8889 + 5.551e-17i) + exp(a*kx*0.25i + a*ky*0.433i)*(0.8889 + 5.551e-17i))
– lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.3333 + 4.082e-17i) – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.8889 – 5.551e-17i) + exp(a*kx*0.5i)*(0.8889 – 5.551e-17i)) + x4*lambda^3*(exp(-a*kx*0.5i)*(0.8889 – 1.11e-16i) + exp(a*kx*0.5i)*(0.8889 – 1.11e-16i)) + x4*lambda^3*(exp(-a*kx*0.5i)*(0.2222 + 2.721e-17i) + exp(a*kx*0.5i)*(0.2222 + 2.721e-17i)), – 0.4444*x4*lambda^3 + (2.0*x1 + 2.0*x2)*lambda, lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.1111 – 0.1925i), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.7778 + 1.347i), lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.6667 – 8.164e-17i) + x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*1.54i – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.4444 – 5.443e-17i) + exp(a*kx*0.5i)*(0.4444 – 5.443e-17i)), 0, lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.6667 – 1.027e-33i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*1.54i – 1.0*x4*lambda^3*(0.4444*exp(- a*kx*0.25i – a*ky*0.433i) + 0.4444*exp(a*kx*0.25i + a*ky*0.433i)), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.6667 – 1.027e-33i) – 0.8889*x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x4*lambda^3*(0.4444*exp(- a*kx*0.25i + a*ky*0.433i) + 0.4444*exp(a*kx*0.25i – a*ky*0.433i))
lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.7778 + 1.347i), lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.1111 + 0.1925i), – 0.4444*x4*lambda^3 + (2.0*x1 + 2.0*x2)*lambda, lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*(0.1111 – 0.1925i), – lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.3333 – 0.5774i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.6667 + 0.3849i) + x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i)*(0.8889 + 1.11e-16i) + exp(a*kx*0.25i – a*ky*0.433i)*(0.8889 + 1.11e-16i)), lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.6667 – 1.027e-33i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(1.257 + 1.54i), 0, 0.6667*lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))) + x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*1.54i – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.4444 – 1.388e-17i) + exp(a*kx*0.5i)*(0.4444 – 1.388e-17i))
lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.1111 – 0.1925i), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.7778 – 1.347i), lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*(0.1111 + 0.1925i), – 0.4444*x4*lambda^3 + (2.0*x1 + 2.0*x2)*lambda, – lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.3333 + 0.5774i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.2222 – 1.155i) – 1.0*x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i)*(0.8889 + 5.551e-17i) + exp(a*kx*0.25i + a*ky*0.433i)*(0.8889 + 5.551e-17i)), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.6667 – 1.027e-33i) – 0.8889*x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x4*lambda^3*(0.4444*exp(- a*kx*0.25i + a*ky*0.433i) + 0.4444*exp(a*kx*0.25i – a*ky*0.433i)), 0.6667*lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))) + x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*1.54i – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.4444 – 1.388e-17i) + exp(a*kx*0.5i)*(0.4444 – 1.388e-17i)), 0
0, lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.6667 + 8.164e-17i) – x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*1.54i – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.4444 + 5.443e-17i) + exp(a*kx*0.5i)*(0.4444 + 5.443e-17i)), – lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.3333 + 0.5774i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.6667 – 0.3849i) + x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i)*(0.8889 – 1.11e-16i) + exp(a*kx*0.25i – a*ky*0.433i)*(0.8889 – 1.11e-16i)), – lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.3333 – 0.5774i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.2222 + 1.155i) – 1.0*x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i)*(0.8889 – 5.551e-17i) + exp(a*kx*0.25i + a*ky*0.433i)*(0.8889 – 5.551e-17i)), – 0.4444*x4*lambda^3 + (2.0*x1 + 2.0*x2)*lambda, – lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.3333 + 4.082e-17i) – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.8889 – 5.551e-17i) + exp(a*kx*0.5i)*(0.8889 – 5.551e-17i)) + x4*lambda^3*(exp(-a*kx*0.5i)*(0.8889 – 1.11e-16i) + exp(a*kx*0.5i)*(0.8889 – 1.11e-16i)) + x4*lambda^3*(exp(-a*kx*0.5i)*(0.2222 + 2.721e-17i) + exp(a*kx*0.5i)*(0.2222 + 2.721e-17i)), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.7778 + 1.347i), lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.1111 – 0.1925i)
lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.6667 + 8.164e-17i) – x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*1.54i – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.4444 + 5.443e-17i) + exp(a*kx*0.5i)*(0.4444 + 5.443e-17i)), 0, lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.6667 + 1.027e-33i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(1.257 – 1.54i), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.6667 + 1.027e-33i) – 0.8889*x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x4*lambda^3*(0.4444*exp(- a*kx*0.25i + a*ky*0.433i) + 0.4444*exp(a*kx*0.25i – a*ky*0.433i)), – lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.3333 – 4.082e-17i) – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.8889 + 5.551e-17i) + exp(a*kx*0.5i)*(0.8889 + 5.551e-17i)) + x4*lambda^3*(exp(-a*kx*0.5i)*(0.8889 + 1.11e-16i) + exp(a*kx*0.5i)*(0.8889 + 1.11e-16i)) + x4*lambda^3*(exp(-a*kx*0.5i)*(0.2222 – 2.721e-17i) + exp(a*kx*0.5i)*(0.2222 – 2.721e-17i)), – 0.4444*x4*lambda^3 + (2.0*x1 + 2.0*x2)*lambda, lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.1111 + 0.1925i), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.7778 – 1.347i)
– lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.3333 + 0.5774i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.6667 – 0.3849i) + x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i)*(0.8889 – 1.11e-16i) + exp(a*kx*0.25i – a*ky*0.433i)*(0.8889 – 1.11e-16i)), lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.6667 + 1.027e-33i) + x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*1.54i – 1.0*x4*lambda^3*(0.4444*exp(- a*kx*0.25i – a*ky*0.433i) + 0.4444*exp(a*kx*0.25i + a*ky*0.433i)), 0, 0.6667*lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))) – x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*1.54i – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.4444 + 1.388e-17i) + exp(a*kx*0.5i)*(0.4444 + 1.388e-17i)), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.7778 – 1.347i), lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.1111 – 0.1925i), – 0.4444*x4*lambda^3 + (2.0*x1 + 2.0*x2)*lambda, lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*(0.1111 + 0.1925i)
– lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.3333 – 0.5774i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.2222 + 1.155i) – 1.0*x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i)*(0.8889 – 5.551e-17i) + exp(a*kx*0.25i + a*ky*0.433i)*(0.8889 – 5.551e-17i)), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.6667 + 1.027e-33i) – 0.8889*x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x4*lambda^3*(0.4444*exp(- a*kx*0.25i + a*ky*0.433i) + 0.4444*exp(a*kx*0.25i – a*ky*0.433i)), 0.6667*lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))) – x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*1.54i – 1.0*x4*lambda^3*(exp(-a*kx*0.5i)*(0.4444 + 1.388e-17i) + exp(a*kx*0.5i)*(0.4444 + 1.388e-17i)), 0, lambda*(x1*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i)) + x2*(exp(- a*kx*0.75i + a*ky*0.433i) + exp(a*kx*0.75i – a*ky*0.433i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i – a*ky*0.433i) + exp(a*kx*0.25i + a*ky*0.433i))*(0.1111 + 0.1925i), lambda*(x1*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i)) + x2*(exp(- a*kx*0.75i – a*ky*0.433i) + exp(a*kx*0.75i + a*ky*0.433i)))*(0.1667 + 0.2887i) – x4*lambda^3*(exp(- a*kx*0.25i + a*ky*0.433i) + exp(a*kx*0.25i – a*ky*0.433i))*(0.7778 + 1.347i), lambda*(x2*(exp(-a*ky*0.866i) + exp(a*ky*0.866i)) + x1*(exp(-a*kx*0.5i) + exp(a*kx*0.5i)))*(0.1667 – 0.2887i) – x4*lambda^3*(exp(-a*kx*0.5i) + exp(a*kx*0.5i))*(0.1111 – 0.1925i), – 0.4444*x4*lambda^3 + (2.0*x1 + 2.0*x2)*lambda
];

FF = F; % this gives same "Uk" on both computers

FF = F + eye(8)*(0.0001); % this gives different "Uk" on both computers

K = chol(FF,"upper");
Q = K*sigma3*(K’); % Q is same on both computers

[RV,D,~] = eig(Q);
[D,I] = sort(diag(real(D)),’descend’);
RV = RV(:, I);
Uk = RV;
Lk = diag(D);

% more specifically i get these results with "FF = F + eye(8)*(0.0001)":

Uk_on_laptop = [-0.5581 – 0.2520i -0.4914 – 0.1718i -0.1074 – 0.3017i 0.2309 – 0.2705i 0.0962 – 0.0850i -0.1447 – 0.2249i 0.1924 – 0.0017i -0.0000 + 0.0000i
0.4717 + 0.2130i -0.5796 – 0.1237i 0.1084 – 0.2927i -0.2900 + 0.2300i -0.2030 + 0.1332i -0.0739 – 0.1924i 0.2089 – 0.0371i 0.0000 + 0.0000i
-0.0445 – 0.4460i -0.0758 – 0.2465i -0.4168 + 0.3376i -0.5328 + 0.0341i -0.2467 – 0.0430i -0.1713 + 0.1603i 0.0220 + 0.2039i 0.0000 – 0.0000i
0.3210 – 0.2306i -0.2904 + 0.1641i 0.3409 + 0.4428i 0.0806 – 0.4949i 0.0400 – 0.2456i 0.1073 + 0.1394i 0.2399 – 0.1355i 0.0000 – 0.0000i
0.0000 – 0.0000i 0.1304 – 0.0722i -0.2064 + 0.0175i 0.0769 – 0.0629i -0.2355 + 0.1429i 0.2359 – 0.0767i 0.2660 – 0.3031i -0.3953 + 0.6846i
-0.0000 + 0.0000i 0.2267 – 0.0899i -0.2537 + 0.0585i -0.1151 + 0.1335i 0.1507 – 0.1648i 0.2370 – 0.2627i 0.4938 – 0.4630i 0.2283 – 0.3953i
-0.0000 – 0.0000i -0.0689 – 0.1710i 0.0363 – 0.2315i 0.0199 + 0.2998i 0.0948 – 0.6211i -0.0523 + 0.5134i -0.0370 – 0.2328i 0.1614 + 0.2795i
-0.0000 + 0.0000i 0.2904 + 0.0000i 0.1855 + 0.0000i 0.2623 + 0.0000i -0.5286 + 0.0000i -0.5890 + 0.0000i 0.3516 + 0.0000i 0.2500 + 0.0000i];

Uk_on_work = [-0.5581 – 0.2520i -0.4914 – 0.1718i -0.1074 – 0.3017i 0.2309 – 0.2705i -0.0962 + 0.0850i -0.1447 – 0.2249i -0.1924 + 0.0017i -0.0000 + 0.0000i
0.4717 + 0.2130i -0.5796 – 0.1237i 0.1084 – 0.2927i -0.2900 + 0.2300i 0.2030 – 0.1332i -0.0739 – 0.1924i -0.2089 + 0.0371i 0.0000 + 0.0000i
-0.0445 – 0.4460i -0.0758 – 0.2465i -0.4168 + 0.3376i -0.5328 + 0.0341i 0.2467 + 0.0430i -0.1713 + 0.1603i -0.0220 – 0.2039i 0.0000 – 0.0000i
0.3210 – 0.2306i -0.2904 + 0.1641i 0.3409 + 0.4428i 0.0806 – 0.4949i -0.0400 + 0.2456i 0.1073 + 0.1394i -0.2399 + 0.1355i 0.0000 – 0.0000i
0.0000 – 0.0000i 0.1304 – 0.0722i -0.2064 + 0.0175i 0.0769 – 0.0629i 0.2355 – 0.1429i 0.2359 – 0.0767i -0.2660 + 0.3031i -0.3953 + 0.6846i
-0.0000 + 0.0000i 0.2267 – 0.0899i -0.2537 + 0.0585i -0.1151 + 0.1335i -0.1507 + 0.1648i 0.2370 – 0.2627i -0.4938 + 0.4630i 0.2283 – 0.3953i
-0.0000 – 0.0000i -0.0689 – 0.1710i 0.0363 – 0.2315i 0.0199 + 0.2998i -0.0948 + 0.6211i -0.0523 + 0.5134i 0.0370 + 0.2328i 0.1614 + 0.2795i
-0.0000 + 0.0000i 0.2904 + 0.0000i 0.1855 + 0.0000i 0.2623 + 0.0000i 0.5286 + 0.0000i -0.5890 + 0.0000i -0.3516 + 0.0000i 0.2500 + 0.0000i];In the following code, when I add the term eye(8)*(0.0001) to the matrix F, my laptop and my work computer return different values for the variable Uk. Could anyone please help me understand what is happening?

I am using MATLAB R2024a on both computers.

clear; clc;

% constants
a = 1;
x1 = 1;
x2 = 0;
x4 = 0;
lambda = 1;

sigma3 = diag([1 1 1 1 -1 -1 -1 -1]);

kx = -2.0944;
ky = -3.6276;

FF = F; % this gives same "Uk" on both computers

FF = F + eye(8)*(0.0001); % this gives different "Uk" on both computers

K = chol(FF,"upper");
Q = K*sigma3*(K’); % Q is same on both computers

[RV,D,~] = eig(Q);
[D,I] = sort(diag(real(D)),’descend’);
RV = RV(:, I);
Uk = RV;
Lk = diag(D);

% more specifically i get these results with "FF = F + eye(8)*(0.0001)":

Uk_on_work = [-0.5581 – 0.2520i -0.4914 – 0.1718i -0.1074 – 0.3017i 0.2309 – 0.2705i -0.0962 + 0.0850i -0.1447 – 0.2249i -0.1924 + 0.0017i -0.0000 + 0.0000i
0.4717 + 0.2130i -0.5796 – 0.1237i 0.1084 – 0.2927i -0.2900 + 0.2300i 0.2030 – 0.1332i -0.0739 – 0.1924i -0.2089 + 0.0371i 0.0000 + 0.0000i
-0.0445 – 0.4460i -0.0758 – 0.2465i -0.4168 + 0.3376i -0.5328 + 0.0341i 0.2467 + 0.0430i -0.1713 + 0.1603i -0.0220 – 0.2039i 0.0000 – 0.0000i
0.3210 – 0.2306i -0.2904 + 0.1641i 0.3409 + 0.4428i 0.0806 – 0.4949i -0.0400 + 0.2456i 0.1073 + 0.1394i -0.2399 + 0.1355i 0.0000 – 0.0000i
0.0000 – 0.0000i 0.1304 – 0.0722i -0.2064 + 0.0175i 0.0769 – 0.0629i 0.2355 – 0.1429i 0.2359 – 0.0767i -0.2660 + 0.3031i -0.3953 + 0.6846i
-0.0000 + 0.0000i 0.2267 – 0.0899i -0.2537 + 0.0585i -0.1151 + 0.1335i -0.1507 + 0.1648i 0.2370 – 0.2627i -0.4938 + 0.4630i 0.2283 – 0.3953i
-0.0000 – 0.0000i -0.0689 – 0.1710i 0.0363 – 0.2315i 0.0199 + 0.2998i -0.0948 + 0.6211i -0.0523 + 0.5134i 0.0370 + 0.2328i 0.1614 + 0.2795i
-0.0000 + 0.0000i 0.2904 + 0.0000i 0.1855 + 0.0000i 0.2623 + 0.0000i 0.5286 + 0.0000i -0.5890 + 0.0000i -0.3516 + 0.0000i 0.2500 + 0.0000i]; In the following code, when I add the term eye(8)*(0.0001) to the matrix F, my laptop and my work computer return different values for the variable Uk. Could anyone please help me understand what is happening?

I am using MATLAB R2024a on both computers.

clear; clc;

% constants
a = 1;
x1 = 1;
x2 = 0;
x4 = 0;
lambda = 1;

sigma3 = diag([1 1 1 1 -1 -1 -1 -1]);

kx = -2.0944;
ky = -3.6276;

FF = F; % this gives same "Uk" on both computers

FF = F + eye(8)*(0.0001); % this gives different "Uk" on both computers

K = chol(FF,"upper");
Q = K*sigma3*(K’); % Q is same on both computers

[RV,D,~] = eig(Q);
[D,I] = sort(diag(real(D)),’descend’);
RV = RV(:, I);
Uk = RV;
Lk = diag(D);

% more specifically i get these results with "FF = F + eye(8)*(0.0001)":

Uk_on_work = [-0.5581 – 0.2520i -0.4914 – 0.1718i -0.1074 – 0.3017i 0.2309 – 0.2705i -0.0962 + 0.0850i -0.1447 – 0.2249i -0.1924 + 0.0017i -0.0000 + 0.0000i
0.4717 + 0.2130i -0.5796 – 0.1237i 0.1084 – 0.2927i -0.2900 + 0.2300i 0.2030 – 0.1332i -0.0739 – 0.1924i -0.2089 + 0.0371i 0.0000 + 0.0000i
-0.0445 – 0.4460i -0.0758 – 0.2465i -0.4168 + 0.3376i -0.5328 + 0.0341i 0.2467 + 0.0430i -0.1713 + 0.1603i -0.0220 – 0.2039i 0.0000 – 0.0000i
0.3210 – 0.2306i -0.2904 + 0.1641i 0.3409 + 0.4428i 0.0806 – 0.4949i -0.0400 + 0.2456i 0.1073 + 0.1394i -0.2399 + 0.1355i 0.0000 – 0.0000i
0.0000 – 0.0000i 0.1304 – 0.0722i -0.2064 + 0.0175i 0.0769 – 0.0629i 0.2355 – 0.1429i 0.2359 – 0.0767i -0.2660 + 0.3031i -0.3953 + 0.6846i
-0.0000 + 0.0000i 0.2267 – 0.0899i -0.2537 + 0.0585i -0.1151 + 0.1335i -0.1507 + 0.1648i 0.2370 – 0.2627i -0.4938 + 0.4630i 0.2283 – 0.3953i
-0.0000 – 0.0000i -0.0689 – 0.1710i 0.0363 – 0.2315i 0.0199 + 0.2998i -0.0948 + 0.6211i -0.0523 + 0.5134i 0.0370 + 0.2328i 0.1614 + 0.2795i
-0.0000 + 0.0000i 0.2904 + 0.0000i 0.1855 + 0.0000i 0.2623 + 0.0000i 0.5286 + 0.0000i -0.5890 + 0.0000i -0.3516 + 0.0000i 0.2500 + 0.0000i]; system, eigenvalue, eig MATLAB Answers — New Questions

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