# Build matrix from smaller matrices or rearange list of lists

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?

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


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

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

• As I mentioned, I am new to this program and I don't know the difference between array an matrix. In my code, I have used "DiagonalMatrix" to crate the basic matrix and then I've used "ReplacePart" to put things in other places in the matrix. So your saing I need to change it to array? – SHBR Oct 28 '18 at 11:47
• No need for special treatment: In Mathematica, matrices are simply arrays (or tensors) of tensor rank 2. And arrays are simply nested Lists of list in rectangular shape. – Henrik Schumacher Oct 28 '18 at 12:38

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.