# How can I multiply matrices using a for loop then extract their elements after the loop?

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Stephen Porter on 28 Nov 2020
Answered: Divija Aleti on 1 Dec 2020
I have calculated a 2x2 matrix, but need to multiply the matrix by itself so many times using a for loop. Then, I want to extract the elements of the matrix following each iteration, use it to calculate something else, and plot the results. I cannot seem to get the values to update the way i want. This is the code I used:
f = 2.88;
ABCD =@(f) [2.44,0.288;(-7.2-(2.44/f)),(-0.44-(0.288/f))]; %ABCD Matrix
M_ABCD = ABCD(f)
A0 = M_ABCD(1,1)
B0 = M_ABCD(1,2)
C0 = M_ABCD(2,1)
D0 = M_ABCD(2,2)
R0 = (2*B0) / (A0 - D0)
Rho0 = (2*B0) / sqrt(4 - ((A0+D0)^2))
Lambda = 0.0001;
W0 = sqrt((Rho0*Lambda)/pi)
q_inv0 = (1/R0) +((j*Lambda)/(pi*(W0^2)));
q0 = 1/q_inv0
%det(M_ABCD)
for i=1:500
M = M_ABCD^(i);
A(i) = M(1,1);
B(i) = M(1,2);
C(i) = M(2,1);
D(i) = M(2,2);
R(i) = (2*B(i)) / (A(i) - D(i));
Rho(i) = (2*B(i)) / sqrt(4 - ((A(i)+D(i))^2));
W(i) = sqrt((Rho(i)*Lambda)/pi);
q_inv(i) = (1/R(i)) +((j*Lambda)/(pi*(W(i)^2)));
q(i) = 1/q_inv(i);
%plot(real(W))
plot(1./R)
end
Walter Roberson on 29 Nov 2020
f = 2.88;
ABCD =@(f) [2.44,0.288;(-7.2-(2.44/f)),(-0.44-(0.288/f))]; %ABCD Matrix
M_ABCD = ABCD(f)
A0 = M_ABCD(1,1)
B0 = M_ABCD(1,2)
C0 = M_ABCD(2,1)
D0 = M_ABCD(2,2)
R0 = (2*B0) / (A0 - D0)
Rho0 = (2*B0) / sqrt(4 - ((A0+D0)^2))
Lambda = 0.0001;
W0 = sqrt((Rho0*Lambda)/pi)
q_inv0 = (1/R0) +((j*Lambda)/(pi*(W0^2)));
q0 = 1/q_inv0
%det(M_ABCD)
M = eye(2);
for i=1:500
M = M * M_ABCD;
A(i) = M(1,1);
B(i) = M(1,2);
C(i) = M(2,1);
D(i) = M(2,2);
R(i) = (2*B(i)) / (A(i) - D(i));
Rho(i) = (2*B(i)) / sqrt(4 - ((A(i)+D(i))^2));
W(i) = sqrt((Rho(i)*Lambda)/pi);
q_inv(i) = (1/R(i)) +((j*Lambda)/(pi*(W(i)^2)));
q(i) = 1/q_inv(i);
end
plot(1./R)
Note that these are only efficiency changes, not changes to any value that would be output. We do not know what output you are expecting so we have no suggestions as to how your original code might somehow be incorrect.
Stephen Porter on 29 Nov 2020
I appericiate the help. I attached a picture of the matrix I am trying to loop over. Basically, I have an inital value of f that will give me an inital values for the entries in the matrix, hence an inital matrix. After each iteration, I want to update the value of f which will update the value of the matrix. So, I need to multiply the new matrix by the previous one with the stating matrix being that initial matrix.
Structure of matrix:
Formula for f (entire denominator will stay constant after each iteration):
Formula for w:
W(i) = sqrt((Rho(i)*Lambda)/pi);
Formula for Rho:
Rho(i) = (2*B(i)) / sqrt(4 - ((A(i)+D(i))^2));
where A(i), B(i), C(i), D(i) are the values of the entries of the ABCD matrix after each iteration.
So, I will calculate each entrie after each iteration, then calcukate Rho, then w, the f, then a new matrix and so on.

Divija Aleti on 1 Dec 2020
Hi Stephen,
I understand that you want to use the elements of the matrix obtained after each iteration to calculate other values and plot the results.
Have a look at the following code, which uses the initial 'f' value to get the initial matrix, extracts its elements, updates the 'f' value in each iteration to get a new matrix and multiplies the new matrix with the previous one and so on.
ABCD =@(f) [2.44,0.288;(-7.2-(2.44/f)),(-0.44-(0.288/f))]; %ABCD Matrix
Lambda = 0.0001;
I0 = 2.43;
n2 = 10.5*10^(-16);
%det(M_ABCD)
f(1) = 2.88;
M = eye(2);
for i=1:500
M_ABCD = ABCD(f(i));
M = M*M_ABCD;
A = M(1,1);
B = M(1,2);
C = M(2,1);
D = M(2,2);
R(i) = (2*B) / (A - D);
Rho(i) = (2*B) / sqrt(4 - ((A+D)^2));
W(i) = sqrt((Rho(i)*Lambda)/pi);
q_inv(i) = (1/R(i)) +((j*Lambda)/(pi*(W(i)^2)));
q(i) = 1/q_inv(i);
f(i+1) = (W(i)^2)/(4*n2*(10^-2)*I0);
stable_check(i) = abs((A+D)/2);
end
figure(1)
subplot(3,1,1)
plot(real(W))
ylabel('W')
subplot(3,1,2)
plot(1./R)
xlabel('Round Trips')
ylabel('R')
subplot(3,1,3)
plot(Rho)
xlabel('Round Trips')
ylabel('Rho')
I hope this helps you get the required output.