linear-algebra

问题 I'm trying to solve the linear equation AX=B where A,X,B are Matrices. I've tried using the np.linalg.solve function of numpy but the result seems to be wrong. Example: Matrix A [9 1 8] [3 2 5] [1 6 5] Matrix B [7 0 5] [7 8 4] [5 6 7] So to solve X, i've used: X = np.linalg.solve(A,B) The result is: X [ 1.17521368 -0.17948718 0.40598291] [ 0.20512821 -0.30769231 0.74358974] [-0.56410256 -0.15384615 1.20512821] But if i try to verify the result by multiplying A by X, the result is anything but

问题 I am trying to write a code that gives me the rotation matrix between two vectors. I have tried the code given as an answer to this question. I first make it calculate the rotation matrix and then test it to see if it gives the correct answer. However, it doesn't seem to be giving the correct answer. Could anyone help with why I can't get the correct answer with this? The Code is below: import numpy as np def rotation_matrix_from_vectors(vec1, vec2): a, b = (vec1 / np.linalg.norm(vec1))

问题 For a finite abelian group G, say, G = AbelianGroup((4,4,5)) , I want Sage to return the automorphism group of G. Is this implemented? 回答1: You can get it partway easily. G = AbelianGroup((4,4,5)) gap(G).AutomorphismGroup() Group( [ Pcgs([ f1, f2, f3, f4, f5 ]) -> [ f1*f3*f4, f2*f4, f3*f4, f4, f5 ], Pcgs([ f1, f2, f3, f4, f5 ]) -> [ f1*f3*f4, f2*f4, f3*f4, f4, f5 ], Pcgs([ f1, f2, f3, f4, f5 ]) -> [ f1, f2, f1*f2*f3, f2*f4, f5 ], Pcgs([ f1, f2, f3, f4, f5 ]) -> [ f1, f2, f2*f3*f4, f4, f5 ],

问题 I have this problem that converting the native sparse format for the QR decomposition of a sparse Matrix takes forever. However, I need it in the CSC format to use it for further computations. using LinearAlgebra, SparseArrays N = 1000 A = sprand(N,N,1e-4) @time F = qr(A) @time F.Q @time Q_sparse = sparse(F.Q) 0.000420 seconds (1.15 k allocations: 241.017 KiB) 0.000008 seconds (6 allocations: 208 bytes) 6.067351 seconds (2.00 M allocations: 15.140 GiB, 36.25% gc time) Any suggestions? 回答1:

问题 In this question was found a solution to find a particular solution to a non-square linear system that has infinitely many solutions. This leads to another question: How to find all the solutions for a non-square linear system with infinitely many solutions, with R? (see below for a possible description of the infinite set of solutions) Example: the linear system x+y+z=1 x-y-2z=2 is equivalent to A X = B with: A=matrix(c(1,1,1,1,-1,-2),2,3,T) B=matrix(c(1,2),2,1,T) A [,1] [,2] [,3] [1,] 1 1 1

问题 In this question was found a solution to find a particular solution to a non-square linear system that has infinitely many solutions. This leads to another question: How to find all the solutions for a non-square linear system with infinitely many solutions, with R? (see below for a possible description of the infinite set of solutions) Example: the linear system x+y+z=1 x-y-2z=2 is equivalent to A X = B with: A=matrix(c(1,1,1,1,-1,-2),2,3,T) B=matrix(c(1,2),2,1,T) A [,1] [,2] [,3] [1,] 1 1 1

问题 I am looking for finding or rather building common eigenvectors matrix X between 2 matrices A and B such as : AX=aX with "a" the diagonal matrix corresponding to the eigenvalues BX=bX with "b" the diagonal matrix corresponding to the eigenvalues where A and B are square and diagonalizable matrices. I took a look in a similar post but had not managed to conclude, i.e having valid results when I build the final wanted endomorphism F defined by : F = P D P^-1 I have also read the wikipedia topic

问题 I am looking for finding or rather building common eigenvectors matrix X between 2 matrices A and B such as : AX=aX with "a" the diagonal matrix corresponding to the eigenvalues BX=bX with "b" the diagonal matrix corresponding to the eigenvalues where A and B are square and diagonalizable matrices. I took a look in a similar post but had not managed to conclude, i.e having valid results when I build the final wanted endomorphism F defined by : F = P D P^-1 I have also read the wikipedia topic

问题 I am looking for finding or rather building common eigenvectors matrix X between 2 matrices A and B such as : AX=aX with "a" the diagonal matrix corresponding to the eigenvalues BX=bX with "b" the diagonal matrix corresponding to the eigenvalues where A and B are square and diagonalizable matrices. I took a look in a similar post but had not managed to conclude, i.e having valid results when I build the final wanted endomorphism F defined by : F = P D P^-1 I have also read the wikipedia topic

问题 In the past when I've needed to solve the Sylvester equation, AX + XB = C , I've used scipy 's function, solve_sylvester [1], which apparently works by using the Bartels-Stewart algorithm to get things into upper triangular form, and then solving the equation using lapack . I now need to solve the equation using eigen . eigen provides an function, matrix_function_solve_triangular_sylvester [2], which seems by the documentation to be similar to the lapack function which scipy calls. I'm