Build matrix from smaller matrices or rearange list of lists

Question

Start with the fact that I am a new user of Mathematica, and this is my problem:

I have a complex simbolic matrix A (rectangular, 14x14), and I want to build a matrix from its imagenary and real parts, such as:

{{A_R, -A_I},{A_I, A_R}}//MatrixForm

I have tried that:

ReV[x_] := Refine[Re[x], _Symbol \[Element] Reals]; 
ImV[x_] := Refine[Im[x], _Symbol \[Element] Reals];
expandedMatrix = {{ReV[A], - ImV[A]}, {ImV[A], ReV[A]}};

But this gives me, under MatrixForm, a matrix of matrices, while I just want a single rectangular matrix which I can use as coefficients matrix of a system of linear equations.

Is there a different way to do that?

Answer 1

n = 2;
A = Array[x, {n, n}] + I Array[y, {n, n}];
A // MatrixForm
B = ComplexExpand[ArrayFlatten[{{Re[A], -Im[A]}, {Im[A], Re[A]}}]];
B // MatrixForm

$$\left( \begin{array}{cc} x(1,1)+ \mathrm{i} \, y(1,1) & x(1,2)+ \mathrm{i} \, y(1,2) \\ x(2,1)+ \mathrm{i} \, y(2,1) & x(2,2)+ \mathrm{i} \, y(2,2) \\ \end{array} \right)$$

$$\left( \begin{array}{cccc} x(1,1) & x(1,2) & -y(1,1) & -y(1,2) \\ x(2,1) & x(2,2) & -y(2,1) & -y(2,2) \\ y(1,1) & y(1,2) & x(1,1) & x(1,2) \\ y(2,1) & y(2,2) & x(2,1) & x(2,2) \\ \end{array} \right)$$

Answer 2

I found a simple way to solve the problem by using the function "Join":

Join[Join[Re[A], - Im[A], 2], Join[Im[A], Re[A], 2]] // MatrixForm

"Join[list1,list2]" concatenates in column direction, while "Join[list1,list2,2]" concatenates in row direction.