#Please do not post homework
#Jeffrey Tang, 2/8/25, Assignment 5

with(linalg)

#RandomState:= inputs positive integers n and K and outputs a vector of length n and values range from -K to K
RandomState := proc(n, K) local v, norm_v, i;
    v := vector(n, i -> evalf(rand(-K..K)() + I*rand(-K..K)())):
    norm_v := sqrt(add(abs(v[i])^2, i=1..n)): 
    (v / norm_v):
end:

#GeneralPauli:= inputs a normalized vector (nx,ny,nz) and outputs a Pauli matrix as outlined in Susskind-Frieman
GeneralPauli := proc(n) local nx, ny, nz, sigma_n;
    nx := n[1]: ny := n[2]: nz := n[3]:
    sigma_n := matrix(2,2, [nz, nx - I*ny, nx + I*ny, -nz]):
    (sigma_n):
end:

#EigenAnalysis:= inputs a matrix A and outputs the eigenvalues and eigenvectors
EigenAnalysis := proc(A)
    local eigenvalues, eigenvectors;
    eigenvalues := eigenvals(A):
    eigenvectors := eigenvectors(A):
    [eigenvalues, eigenvectors]:
end proc: