nx_matrix_eig_gate.nx

nx_matrix_eig_gate.nx -- AM1: DOES THE SYMMETRIC EIGENSOLVER ACTUALLY SOLVE, AND CAN IT REFUSE? The done-rule was pre-declared on /compare/appliedmath before a line of the solver was written: "reconstructing the matrix from its factors returns the original within the declared bound, the eigenvalues of a known symmetric matrix match their exact values, and a singular matrix is reported singular rather than inverted" so these teeth are the rule being met rather than a rule written to fit what the code happens to do. EVERY TOOTH IS AN INVARIANT OF THE EIGENPROBLEM, NOT A STORED ANSWER. Trace equals the sum of the eigenvalues; a diagonal matrix has its own diagonal as its spectrum; eigenvectors of a symmetric matrix are orthonormal; and the residual max|AV - VL| is the bound the reference libraries publish. A stored golden vector would record that the author agreed with the code on one afternoon; these hold for any correct implementation and fail for any wrong one. license_tier: ORIGINAL expect_exit: 0