enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  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. QR algorithm - Wikipedia

    en.wikipedia.org/wiki/QR_algorithm

    In numerical linear algebra, the QR algorithm or QR iteration is an eigenvalue algorithm: that is, a procedure to calculate the eigenvalues and eigenvectors of a matrix.The QR algorithm was developed in the late 1950s by John G. F. Francis and by Vera N. Kublanovskaya, working independently.

  4. Inverse iteration - Wikipedia

    en.wikipedia.org/wiki/Inverse_iteration

    In such applications, typically the statistics of matrices is known in advance and one can take as an approximate eigenvalue the average eigenvalue for some large matrix sample. Better, one may calculate the mean ratio of the eigenvalues to the trace or the norm of the matrix and estimate the average eigenvalue as the trace or norm multiplied ...

  5. Eigenvalues and eigenvectors - Wikipedia

    en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

    In spectral graph theory, an eigenvalue of a graph is defined as an eigenvalue of the graph's adjacency matrix, or (increasingly) of the graph's Laplacian matrix due to its discrete Laplace operator, which is either (sometimes called the combinatorial Laplacian) or / / (sometimes called the normalized Laplacian), where is a diagonal matrix with ...

  6. Eigendecomposition of a matrix - Wikipedia

    en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix

    Let A be a square n × n matrix with n linearly independent eigenvectors q i (where i = 1, ..., n).Then A can be factored as = where Q is the square n × n matrix whose i th column is the eigenvector q i of A, and Λ is the diagonal matrix whose diagonal elements are the corresponding eigenvalues, Λ ii = λ i.

  7. 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.

  8. Eigenfunction - Wikipedia

    en.wikipedia.org/wiki/Eigenfunction

    Functions can be written as a linear combination of the basis functions, = = (), for example through a Fourier expansion of f(t). The coefficients b j can be stacked into an n by 1 column vector b = [b 1 b 2 … b n] T. In some special cases, such as the coefficients of the Fourier series of a sinusoidal function, this column vector has finite ...

  9. Square root of a matrix - Wikipedia

    en.wikipedia.org/wiki/Square_root_of_a_matrix

    A matrix B is said to be a square root of A if the matrix product BB is equal to A. [ 1 ] Some authors use the name square root or the notation A 1/2 only for the specific case when A is positive semidefinite , to denote the unique matrix B that is positive semidefinite and such that BB = B T B = A (for real-valued matrices, where B T is the ...