plummie

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These are replies submitted by plummie

though that sounds like it would be a great idea. I'm not sure how I could implement it as I would have to generate new lists for each i from 1 to n, then put the result of smallestRealDiff into a new list.

I don't think that when I'm generating things for upto i=200 this would work very well as I'd have to write a load of new loops around it and I think that would confuse me more.

though that sounds like it would be a great idea. I'm not sure how I could implement it as I would have to generate new lists for each i from 1 to n, then put the result of smallestRealDiff into a new list.

I don't think that when I'm generating things for upto i=200 this would work very well as I'd have to write a load of new loops around it and I think that would confuse me more.

I just tried inputting that into maple. Again I got given strange eigenvalues of the from a + b*10^-17*I

which is exactly the form I was getting previously. (with my home made matrix)

I just tried inputting that into maple. Again I got given strange eigenvalues of the from a + b*10^-17*I

which is exactly the form I was getting previously. (with my home made matrix)

Using this maple does not give me the correct eigenvalues. I have also seen this when creating my own normal hermitian matrix from scratch using:
 

for i to 2 do

for j to 2 do

if i <> j then A[i, j] := I*Generate(distribution(Normal(0, .5))); A[j, i] := -A[i, j]; B[i, j] := Generate(distribution(Normal(0, .5))); B[j, i] := B[i, j] end if;

if i = j then B[i, j] := Generate(distribution(Normal(0, 1))) end if

end do end do;

C := A+B
 

Maple gives me evalues which are a combination of real and imaginary numbers which is obviously incorrect as hermitian matrices have real eigenvalues. I also need my off diagonal entries to be distributed N(0,0.5)+IN(0,0.5)

Please can anyone help? I really need to figure this out properly by the end of the day

Using this maple does not give me the correct eigenvalues. I have also seen this when creating my own normal hermitian matrix from scratch using:
 

for i to 2 do

for j to 2 do

if i <> j then A[i, j] := I*Generate(distribution(Normal(0, .5))); A[j, i] := -A[i, j]; B[i, j] := Generate(distribution(Normal(0, .5))); B[j, i] := B[i, j] end if;

if i = j then B[i, j] := Generate(distribution(Normal(0, 1))) end if

end do end do;

C := A+B
 

Maple gives me evalues which are a combination of real and imaginary numbers which is obviously incorrect as hermitian matrices have real eigenvalues. I also need my off diagonal entries to be distributed N(0,0.5)+IN(0,0.5)

Please can anyone help? I really need to figure this out properly by the end of the day

I have looked at doing it in one step but my off diagonal values have a different normal distribution to the diagonals and the matrix has to be hermitian. One way I did find to do it didn't allow me to generate eigenvalues of a large n x n case so I'm now attempting to build the matrix from scratch by generating values of each distribution and inputting them in the matrix using a for loop.

Obviously if there is a simpler way to do it, then I would appreciate your help.

 

I have looked at doing it in one step but my off diagonal values have a different normal distribution to the diagonals and the matrix has to be hermitian. One way I did find to do it didn't allow me to generate eigenvalues of a large n x n case so I'm now attempting to build the matrix from scratch by generating values of each distribution and inputting them in the matrix using a for loop.

Obviously if there is a simpler way to do it, then I would appreciate your help.

 

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