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2. Eigenvalue algorithm - Wikipedia

   en.wikipedia.org/wiki/Eigenvalue_algorithm

   Given an n × n square matrix A of real or complex numbers, an eigenvalue λ and its associated generalized eigenvector v are a pair obeying the relation [1] =,where v is a nonzero n × 1 column vector, I is the n × n identity matrix, k is a positive integer, and both λ and v are allowed to be complex even when A is real.l When k = 1, the vector is called simply an eigenvector, and the pair ...

3. Eigenvalues and eigenvectors - Wikipedia

   en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

   The corresponding eigenvalue, characteristic value, or characteristic root is the multiplying factor (possibly negative). Geometrically, vectors are multi-dimensional quantities with magnitude and direction, often pictured as arrows. A linear transformation rotates, stretches, or shears the vectors upon which it acts. Its eigenvectors are those ...

4. Jacobi eigenvalue algorithm - Wikipedia

   en.wikipedia.org/wiki/Jacobi_eigenvalue_algorithm

   In numerical linear algebra, the Jacobi eigenvalue algorithm is an iterative method for the calculation of the eigenvalues and eigenvectors of a real symmetric matrix (a process known as diagonalization).

5. Jacobian matrix and determinant - Wikipedia

   en.wikipedia.org/wiki/Jacobian_matrix_and...

   Specifically, if the eigenvalues all have real parts that are negative, then the system is stable near the stationary point. If any eigenvalue has a real part that is positive, then the point is unstable. If the largest real part of the eigenvalues is zero, the Jacobian matrix does not allow for an evaluation of the stability. [12]

6. Arnoldi iteration - Wikipedia

   en.wikipedia.org/wiki/Arnoldi_iteration

   In numerical linear algebra, the Arnoldi iteration is an eigenvalue algorithm and an important example of an iterative method.Arnoldi finds an approximation to the eigenvalues and eigenvectors of general (possibly non-Hermitian) matrices by constructing an orthonormal basis of the Krylov subspace, which makes it particularly useful when dealing with large sparse matrices.

7. Symbolab - Wikipedia

   en.wikipedia.org/wiki/Symbolab

   Symbolab is an answer engine [1] that provides step-by-step solutions to mathematical problems in a range of subjects. [2] It was originally developed by Israeli start-up company EqsQuest Ltd., under whom it was released for public use in 2011. In 2020, the company was acquired by American educational technology website Course Hero. [3] [4]

8. Rayleigh–Ritz method - Wikipedia

   en.wikipedia.org/wiki/Rayleigh–Ritz_method

   In numerical linear algebra, the Rayleigh–Ritz method is commonly [12] applied to approximate an eigenvalue problem = for the matrix of size using a projected matrix of a smaller size <, generated from a given matrix with orthonormal columns. The matrix version of the algorithm is the most simple:

9. Generalized eigenvector - Wikipedia

   en.wikipedia.org/wiki/Generalized_eigenvector

   In linear algebra, a generalized eigenvector of an matrix is a vector which satisfies certain criteria which are more relaxed than those for an (ordinary) eigenvector. [1]Let be an -dimensional vector space and let be the matrix representation of a linear map from to with respect to some ordered basis.