enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Positive semidefinite - Wikipedia

    en.wikipedia.org/wiki/Positive_semidefinite

    In mathematics, positive semidefinite may refer to: Positive semidefinite function; Positive semidefinite matrix; Positive semidefinite quadratic form;

  3. Normal matrix - Wikipedia

    en.wikipedia.org/wiki/Normal_matrix

    U and P commute, where we have the polar decomposition A = UP with a unitary matrix U and some positive semidefinite matrix P. A commutes with some normal matrix N with distinct [clarification needed] eigenvalues. σ i = | λ i | for all 1 ≤ i ≤ n where A has singular values σ 1 ≥ ⋯ ≥ σ n and has eigenvalues that are indexed with ...

  4. Conjugate gradient method - Wikipedia

    en.wikipedia.org/wiki/Conjugate_gradient_method

    The conjugate gradient method can be applied to an arbitrary n-by-m matrix by applying it to normal equations A T A and right-hand side vector A T b, since A T A is a symmetric positive-semidefinite matrix for any A. The result is conjugate gradient on the normal equations (CGN or CGNR). A T Ax = A T b

  5. Definite matrix - Wikipedia

    en.wikipedia.org/wiki/Definite_matrix

    In mathematics, a symmetric matrix with real entries is positive-definite if the real number is positive for every nonzero real column vector , where is the row vector transpose of . [1] More generally, a Hermitian matrix (that is, a complex matrix equal to its conjugate transpose) is positive-definite if the real number is positive for every nonzero complex column vector , where denotes the ...

  6. Gram matrix - Wikipedia

    en.wikipedia.org/wiki/Gram_matrix

    The Gram matrix is positive semidefinite, and every positive semidefinite matrix is the Gramian matrix for some set of vectors. The fact that the Gramian matrix is positive-semidefinite can be seen from the following simple derivation:

  7. Hessian matrix - Wikipedia

    en.wikipedia.org/wiki/Hessian_matrix

    This implies that at a local minimum the Hessian is positive-semidefinite, and at a local maximum the Hessian is negative-semidefinite. For positive-semidefinite and negative-semidefinite Hessians the test is inconclusive (a critical point where the Hessian is semidefinite but not definite may be a local extremum or a saddle point).

  8. Non-negative least squares - Wikipedia

    en.wikipedia.org/wiki/Non-negative_least_squares

    Set P = ∅. Set R = {1, ..., n}. Set x to an all-zero vector of dimension n. Set w = A T (y − Ax). Let w R denote the sub-vector with indexes from R; Main loop: while R ≠ ∅ and max(w R) > ε: Let j in R be the index of max(w R) in w. Add j to P. Remove j from R. Let A P be A restricted to the variables included in P. Let s be vector of ...

  9. Fisher information - Wikipedia

    en.wikipedia.org/wiki/Fisher_information

    The FIM is a N × N positive semidefinite matrix. If it is positive definite, then it defines a Riemannian metric [11] on the N-dimensional parameter space. The topic information geometry uses this to connect Fisher information to differential geometry, and in that context, this metric is known as the Fisher information metric.