Let AA be an n×nn×n matrix. If there exists an n×nn×n invertible matrix PP and a diagonal matrix DD, such that A=PDP−1A=PDP−1 then matrix AA is called a diagonalizable matrix. And futher, the columns of PP are linearly independent eigenvectors of AA, and its corresponding ...
In the previous two cases, ChatGPT explained the algorithm to perform an (orthogonal) diagonalization of a matrix. In this case, it directly provided a Python code and its corresponding output. Furthermore, although the original matrix contains integer entries, the matrices in its SVD consist of...
importnumpyasnpfromqndiagimportqndiagn,p=10,3diagonals=np.random.uniform(size=(n,p))A=np.random.randn(p,p)# mixing matrixC=np.array([A.dot(d[:,None]*A.T)fordindiagonals])# datasetB,_=qndiag(C)# use the algorithmprint(B.dot(A))# Should be a permutation + scale matrix ...
This is a Python library to compute quasi-one-dimensional spin chains and fermionic systems using matrix product states with the density matrix renormalization group as implemented in ITensor (C++ and Julia versions). Most of the computations can be performed both with DMRG and exact diagonalization...