MATLAB: Sub-Matrices in a bigger matrix

composing the matrices

Dear Users,

Imagine that I have 4 square matrices such as A11, B11, C11 and D22.

I want to insert them as diagonal elements of a bigger matrix (please see the pic on the attchments).

However, I don't know the size of the bigger matrix. I will find it out when I insert all sub-matrices. Is there any easy way to do it?

Thanks in advance!

Best Answer

blkdiag(A11, B11, C11, D22)

Related Solutions

MATLAB: How to solve this Matrix Equation

The solution is definitely not unique.

Let the two result matrices be [rab11,0;0,rab22] and [rcd11;0;0;rcd22]

Set rcd22 to any non-zero non-infinite value. Then, except for possible singularities,

rab11 = rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))

rab22 = -rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21))

rcd11 = -rcd22*((d11*c11*(b11*b22-b12*b21)*a22-a21*c12*b12*(b11*d21-b21*d11))*a12+a11*a22*b11*c12*(b12*d21-d11*b22))/((c21*d12*(b11*b22-b12*b21)*a22-a21*c22*b12*(b11*d22-b21*d12))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))

You can see in this that rcd22 acts as an arbitrary scale factor for the other coefficients.

The X matrix then becomes

X(1,1) = (b22*a22*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))-b22*a12*rab21-b21*a22*rab12-b21*a12*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21)))/((a11*a22-a12*a21)*(b11*b22-b12*b21))

X(1,2) = -(b12*a22*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))-b12*a12*rab21-b11*a22*rab12-b11*a12*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21)))/((a11*a22-a12*a21)*(b11*b22-b12*b21))

X(2,1) = -(b22*a21*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))-b22*a11*rab21-b21*a21*rab12-b21*a11*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21)))/((a11*a22-a12*a21)*(b11*b22-b12*b21))

X(2,2) = -(b22*a21*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b11+b21*d12*d11*(c11*c22-c12*c21))*a12+a11*b11*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((d12*c21*b22*a22-b12*a21*d22*c22)*b11+d12*b12*b21*(-c21*a22+a21*c22))*a12+a11*a22*b11*c22*(-d12*b22+b12*d22))*(c11*c22-c12*c21)*(d11*d22-d12*d21))-b22*a11*rab21-b21*a21*rab12-b21*a11*rcd22*(((c12*c21*d12*d21-c11*c22*d11*d22)*b12+b22*d12*d11*(c11*c22-c12*c21))*a22+a21*b12*c12*c22*(d11*d22-d12*d21))*(a11*a22-a12*a21)*(b11*b22-b12*b21)/((((b11*d22*c22*a11-d12*c21*a12*b21)*b12-d12*b11*b22*(c22*a11-a12*c21))*a22-a12*a21*c22*b12*(b11*d22-b21*d12))*(c11*c22-c12*c21)*(d11*d22-d12*d21)))/((a11*a22-a12*a21)*(b11*b22-b12*b21))

This was calculated using straight-forward linear algebra by multiplying appropriate inverses on both sides to get two isolated X equations, and then solve()'ing for the corresponding components to be the same.

MATLAB: Matrix Elements Manipulation Using Matlab

a=zeros(4,7);
a(:,1:2:end)=A;
a(:,2:2:end)=B;
b=zeros(3,7);
b(:,1:2:end)=C;
b(:,2:2:end)=D;
out=zeros(7);
out(1:2:end,:)=a;
out(2:2:end,:)=b

Best Answer

Related Solutions

MATLAB: How to solve this Matrix Equation

MATLAB: Matrix Elements Manipulation Using Matlab

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