enow.com Web Search

Search results

  1. Results from the WOW.Com Content Network
  2. Matrix norm - Wikipedia

    en.wikipedia.org/wiki/Matrix_norm

    The Frobenius norm is an extension of the Euclidean norm to and comes from the Frobenius inner product on the space of all matrices. The Frobenius norm is sub-multiplicative and is very useful for numerical linear algebra. The sub-multiplicativity of Frobenius norm can be proved using Cauchy–Schwarz inequality.

  3. Frobenius normal form - Wikipedia

    en.wikipedia.org/wiki/Frobenius_normal_form

    On the other hand, this makes the Frobenius normal form rather different from other normal forms that do depend on factoring the characteristic polynomial, notably the diagonal form (if A is diagonalizable) or more generally the Jordan normal form (if the characteristic polynomial splits into linear factors). For instance, the Frobenius normal ...

  4. Trace (linear algebra) - Wikipedia

    en.wikipedia.org/wiki/Trace_(linear_algebra)

    The norm derived from this inner product is called the Frobenius norm, and it satisfies a submultiplicative property, as can be proven with the Cauchy–Schwarz inequality: [⁡ ()] ⁡ ⁡ , if A and B are real matrices such that A B is a square matrix.

  5. Frobenius matrix - Wikipedia

    en.wikipedia.org/wiki/Frobenius_matrix

    A Frobenius matrix is a special kind of square matrix from numerical analysis. A matrix is a Frobenius matrix if it has the following three properties: all entries on the main diagonal are ones; the entries below the main diagonal of at most one column are arbitrary; every other entry is zero; The following matrix is an example.

  6. Dual norm - Wikipedia

    en.wikipedia.org/wiki/Dual_norm

    The Frobenius norm defined by ‖ ‖ = = = | | = ⁡ = = {,} is self-dual, i.e., its dual norm is ‖ ‖ ′ = ‖ ‖.. The spectral norm, a special case of the induced norm when =, is defined by the maximum singular values of a matrix, that is, ‖ ‖ = (), has the nuclear norm as its dual norm, which is defined by ‖ ‖ ′ = (), for any matrix where () denote the singular values ...

  7. Singular value decomposition - Wikipedia

    en.wikipedia.org/wiki/Singular_value_decomposition

    After the algorithm has converged, the singular value decomposition = is recovered as follows: the matrix is the accumulation of Jacobi rotation matrices, the matrix is given by normalising the columns of the transformed matrix , and the singular values are given as the norms of the columns of the transformed matrix .

  8. Frobenius inner product - Wikipedia

    en.wikipedia.org/wiki/Frobenius_inner_product

    Matrix norm; Tensor product of Hilbert spaces – the Frobenius inner product is the special case where the vector spaces are finite-dimensional real or complex vector spaces with the usual Euclidean inner product

  9. Matrix regularization - Wikipedia

    en.wikipedia.org/wiki/Matrix_regularization

    One example is the squared Frobenius norm, which can be viewed as an -norm acting either entrywise, or on the singular values of the matrix: = ‖ ‖ = | | = ⁡ =. In the multivariate case the effect of regularizing with the Frobenius norm is the same as the vector case; very complex models will have larger norms, and, thus, will be penalized ...