You can also explore eigenvectors, characteristic polynomials, invertible matrices, diagonalization and many other matrix-related topics. H0 is a compiled function which sped things up a little.Ģ Sqrt)}, ],Parallelization -> True] ĭoes give the correct output, however again Listable provides problems for EigenSystem once parallel input is provided. Math Input Vectors & Matrices More than just an online eigenvalue calculator WolframAlpha is a great resource for finding the eigenvalues of matrices. Given a possibly coupled partial differential equation (PDE), a region specification, and, optionally, boundary conditions, the eigensolvers find corresponding. (*elements of v and vS are called later v], vS] etc.*) Version 11 extends its symbolic and numerical differential equation-solving capabilities to include finding eigenvalues and eigenfunctions over regions. In the line Number of digits displayed in output, set the preferred precision. Select the tab Appearance Numbers Formatting. r = RandomReal, 6] Įs = Eigensystem], r], r], r], r], r] ] Navigate to the menu item Edit Preferences on Windows or Mathematica Preferences on Mac. Currently, it is taking several hours to run so I am hoping that I can cut down some runtime with your help. Which of the eigendecomposition or the Schur decomposition should you use depends on what you really want to do, which you haven't mentioned.I have a module that I need to call 1-10 million times in my program. There are applications where it is better to have a Schur decomposition than an eigendecomposition (and a Schur decomposition certainly takes less effort to compute, as well as less susceptible to numerical instability). For instance: Eigenvalues[$, with $\mathbf Q,\mathbf P$ unitary/orthogonal and $\mathbf S,\mathbf T$ upper (quasi-)triangular (depending on the setting of the option RealBlockDiagonalForm), and $\dagger$ denoting a Hermitian (conjugate) transpose. Eigenvalues/ Eigenvectors/ Eigensystem, as well as CharacteristicPolynomial and SchurDecomposition, are all able to handle matrix pencils, as long as the matrix contains inexact elements. If L is a linear operator on a function space, then f is an eigenfunction for L and lambda is the associated eigenvalue whenever Lflambdaf. Mathematica is quite capable of computing the eigenvalues of matrix pencils (i.e., the generalized eigenproblem).
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