FOR loop with matrices

I am working on coding a problem where we have Matrix A (3x3) and vector x0 (3x1).

x(k+1) = A*x0 where k =0 this new x vector will then be multiplied to A

so x(1+1)= A*x1 and so on.

the only thing staying constant is A matrix with the vector x changing. But i want to store and keep each vector x.

I am having troubles writing this.

[Jan]

Please post, what you have tried so far. It needs only 3 lines and it is not clear if this is a homework problem.

[James Tursa]

Do you want A*x0, (A^2)*x0, (A^3)*x0, etc, and all the results stored in a single result matrix?

[jtruxal]

James that is not what I want.

Matrix A is a 3x3 that will always containt the same elements.

Vector x0 (3x1) is the "initializer"

I want to multiply A*xk=xk+1

So first would be A*x0=x1

Then A*x1=x2 and so on.

Jan ---> I have

A = [3x3 stuff]

x0 = [3x1 stuff]

for k=0:10

x(k+1)=A*x(k)

i cant figure how to continue the for loop so it takes x1 and keeps running it

Answer 1

[Jan]

A = rand(3, 3);
x = rand(3, 1);
v = zeros(11, 3);  % Pre-allocation!

v(1, :) = x;
for k = 1:10
  v(k + 1, :) = A * v(k, :);
end

Then the vectors x_i are stores as columns of the matix v. Another approach with a cell:

v    = cell(1, 11);  % pre-allocation!
v{1} = x;
for k = 1:10
  v{k + 1} = A * v{k};
end

Btw., look at James' comment again:

x1 = A * x0
x2 = A * x1 = A * A * x0 = A^2 * x0
x3 = A * x2 = ...        = A^3 * x0
...

[jtruxal]

My apologies James. I did not think of doing it this way.

That would work. However, I would want to store the results in different vectors.

The vectors x1, x2, x3 ... are the ones I want to compare.

I guess my question with James approach is how would you store the vectors using a for loop with his equation because it would be

xn = A^n * x0 right?

[jtruxal]

this is what i have so far but i keep getting an error

A = [.70,.15,.10;.15,.80,.30;.15,.05,.60]

x0 = [300;350;200]

for n = 1:10

x(n) = A^(n) * x0

end

error: In an assignment A(I) = B, the number of elements in B and

I must be the same.

[Andrei Bobrov]

for n = 10:-1:1

x(:,n) = A^(n) * x0

end

[jtruxal]

and what if i didnt want to store it in a matrix but instead individual vectors x1, x2, x3 ...

[Andrei Bobrov]

this is bad way

please read http://matlab.wikia.com/wiki/FAQ#How_can_I_create_variables_A1.2C_A2.2C....2CA10_in_a_loop.3F

[Jan]

x{1}, x{2}, ... is a good way to store the individual vectors. It is a bad idea, to hide the index in the name of the variable, because complicated methods to create complicated names of variables require further complicated methdos to access these variables later.