enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Eigenvalues and eigenvectors - Wikipedia

    en.wikipedia.org/wiki/Eigenvalues_and_eigenvectors

    For defective matrices, the notion of eigenvectors generalizes to generalized eigenvectors and the diagonal matrix of eigenvalues generalizes to the Jordan normal form. Over an algebraically closed field, any matrix A has a Jordan normal form and therefore admits a basis of generalized eigenvectors and a decomposition into generalized eigenspaces .

  3. Principal component analysis - Wikipedia

    en.wikipedia.org/wiki/Principal_component_analysis

    The eigenvalues and eigenvectors are ordered and paired. The jth eigenvalue corresponds to the jth eigenvector. Matrix V denotes the matrix of right eigenvectors (as opposed to left eigenvectors). In general, the matrix of right eigenvectors need not be the (conjugate) transpose of the matrix of left eigenvectors. Rearrange the eigenvectors and ...

  4. Eigendecomposition of a matrix - Wikipedia

    en.wikipedia.org/wiki/Eigendecomposition_of_a_matrix

    The eigenvalues are real. The eigenvectors of A −1 are the same as the eigenvectors of A. Eigenvectors are only defined up to a multiplicative constant. That is, if Av = λv then cv is also an eigenvector for any scalar c ≠ 0. In particular, −v and e iθ v (for any θ) are also eigenvectors.

  5. Spectrum of a matrix - Wikipedia

    en.wikipedia.org/wiki/Spectrum_of_a_matrix

    Thus the elements of the spectrum are precisely the eigenvalues of T, and the multiplicity of an eigenvalue λ in the spectrum equals the dimension of the generalized eigenspace of T for λ (also called the algebraic multiplicity of λ). Now, fix a basis B of V over K and suppose M ∈ Mat K (V) is a matrix.

  6. 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 ...

  7. Phase plane - Wikipedia

    en.wikipedia.org/wiki/Phase_plane

    The signs of the eigenvalues indicate the phase plane's behaviour: If the signs are opposite, the intersection of the eigenvectors is a saddle point. If the signs are both positive, the eigenvectors represent stable situations that the system diverges away from, and the intersection is an unstable node.

  8. 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.

  9. Eigenvalues and eigenvectors

    en.wikipedia.org/.../Eigenvalues_and_eigenvectors

    In linear algebra, it is often important to know which vectors have their directions unchanged by a given linear transformation. An eigenvector (/ ˈ aɪ ɡ ən-/ EYE-gən-) or ch