Appending a column to a matrix in a for loop.

So the task that I am trying to complete is as follows: write a script that starts with a random m vector, and apply the HilbertMatrix (HilbertMatrix(m)) to it N times, saving the result of the n-th multiplication as the n-th column of a matrix V. This is what I have so far:

r = randi([1 100],1,1);         %Choose a random number "r" between 1 and 100. 
m = randi([1 100],r,1);         %Create a vector "m" with dimensions rx1 i.e. a random vector. 
H = HilbertMatrix(r);           %Create a Hilbert matrix of size rxr. 

for i=1:N                       %For every i, you multiply the vector by the Hilbert matrix. 
    v = H^(i).*m;               %Your result goes to the the 1st column of a new matrix. 
    V = [V v];                  %You continue so that the n-th multiplication of the Hilbert with the vector goes to the nth column. 
end

disp(V)                         %Show the matrix.

I seem to be getting a few errors. I feel though that my logic is there. I am new to MATLAB but have had exeprience with Python. Hopefully, they are syntax errors. Here is my HilbertMatrix function code:

function h = HilbertMatrix(m)

H = zeros(m,m)                      %Create an empty mxm matrix. 
for k=1:m
    for j=1:m
        H(j,k)=1/(j+k-1)            %Definition of the Hilbert Matrix. 
        H(k,j)=H(j,k)               %Entries of a Hilbert Matrix are symmetric along the diagonal. 
    end
end

end

Any and all help will be greatly appreciated. Thank you!

[Andrew You]

My Hilbert function is correct. I ran the function for different n-values and the entries were correct. I believe my script is in need of work.

Answer 1

[Pierre Benoit]

First, about your function, there is a problem with the output because Matlab is case sensitive. Replace h with H.

Then for your script, ".*" is element-wise multiplication, not matix multiplication. It's simply * Also, you didn't define V before using it, you try to concatenate an undefined vector with v. You could do

V = zeros(r,N);
for i=1:N                       %For every i, you multiply the vector by the Hilbert matrix. 
    V(:,i) = H^(i)*m;               %Your result goes to the the ist column of a new matrix. 
end

Now, this should work. Let me know if I misunderstood something or if there is something wrong.

[Julia]

Sorry, I only saw your answer after submitting my own!

Answer 2

[Julia]

Hi,

(I am writing this while trying to debug your code ;) )

- Your function HilbertMatrix() returns only a zero-matrix. Your output is "h" but you compute "H".

- You never define "N" (upper limit of the loop).

- Then you get an error for

v = H^(i).*m;

--> delete the point:

   v = H^(i)*m;

- And finally you have to initialize V before using it. You write

V = [V v];

But in the first iteration there is no V.

My solution was:

v = H*m;              
V = v;

and start the loop with i=2

I hope this yields the right result.