# Questions tagged [eigenvalues]

Eigenvalues are a special set of scalars associated with a linear system of equations (i.e., a matrix equation) that are sometimes also known as characteristic roots, characteristic values (Hoffman and Kunze 1971), proper values, or latent roots (Marcus and Minc 1988, p. 144).

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I am trying to compute the natural frequency of a cantilevered beam. The Euler-Bernoulli equation reduces to the following problem : $$v''''=\lambda v, \text{with }, v(0)=0, v'(0)=0, v'''(1)=0,v''(1)... 0 votes 1 answer 110 views ### How are eigenvalues of a cell in the finite volume discretization calculated? (for euler fluid equations) I am building a program to numerically solve the euler fluid equations based on finite volume discretization and am having trouble on a step where the eigenvalues of a cell need to be calculated ... 3 votes 0 answers 119 views ### Does shift-invert method has invertibility issue? Please note that I have nearly zero background on numerical methods. I understand the shift invert method as described in SciPy Tutorial The main argument of the above link is as follows. Suppose we ... 2 votes 4 answers 860 views ### Eigenvalue decomposition for a very huge matrix of medical images (such as the pixel physical coordinates of CT images) I am trying to do eigenvalue decomposition for a huge matrix larger than 788000×788000 for medical image analysis. The matrix is not sparse and every element in the matrix has a real value. And, for ... 0 votes 1 answer 311 views ### Pseudospectrum of non square Matrix in Python I have a rectangular matrix A \in \mathbb{R}^{m \times n} ... 3 votes 1 answer 326 views ### Lanczos algorithm for finding top eigenvalues of a matrix sum I am trying to find the top k leading eigenvalues of a NumPy matrix (using python dot product notation) L@L + a*[email protected], where L ... 0 votes 0 answers 488 views ### Numerical Range of a matrix in Python In the mathematical field of linear algebra and convex analysis, the numerical range or field of values of a complex n\times n matrix A is the set$$W(A)=\left\{{\frac {{\mathbf {x}}^{*}A{\... 122 views

### Large scale nonsymmetric eigenvalue problems in practical applications

I am trying to determine need for solving large scale nonsymmetric eigenvalue problems in both industry and academia. I am interested in any kind of problem where we cannot assume that matrices are ...
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### Given a symmetric matrix, is it ok to apply Cholesky decomposition to see if it has negative eigenvalues?

I intend to check the diagonal of L, where A = L'L, for negative elements. However, I don't know if Cholesky is meaningful in theoretical / computational sense if there are some negative eigenvalues.
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### Neural networks trained with subspace iteration algorithms for solving SCF eigenvalue problems

I am toying with the idea of using current libraries available with SCF (Self-Consistent Field) subspace iteration codes to train an ANN (Artificial Neural Network) to solve for SCF eigenvalue ... 