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  2. Positive semidefinite - Wikipedia

    en.wikipedia.org/wiki/Positive_semidefinite

    Download as PDF; Printable version; In other projects ... move to sidebar hide. In mathematics, positive semidefinite may refer to: Positive semidefinite function ...

  3. Positive operator - Wikipedia

    en.wikipedia.org/wiki/Positive_operator

    In mathematics (specifically linear algebra, operator theory, and functional analysis) as well as physics, a linear operator acting on an inner product space is called positive-semidefinite (or non-negative) if, for every ⁡ (), , and , , where ⁡ is the domain of .

  4. Positive-definite function - Wikipedia

    en.wikipedia.org/wiki/Positive-definite_function

    Positive-definiteness arises naturally in the theory of the Fourier transform; it can be seen directly that to be positive-definite it is sufficient for f to be the Fourier transform of a function g on the real line with g(y) ≥ 0.

  5. 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).

  6. 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 ...

  7. Diagonally dominant matrix - Wikipedia

    en.wikipedia.org/wiki/Diagonally_dominant_matrix

    A Hermitian diagonally dominant matrix with real non-negative diagonal entries is positive semidefinite. This follows from the eigenvalues being real, and Gershgorin's circle theorem. If the symmetry requirement is eliminated, such a matrix is not necessarily positive semidefinite. For example, consider

  8. Gram matrix - Wikipedia

    en.wikipedia.org/wiki/Gram_matrix

    The Gram matrix is symmetric in the case the inner product is real-valued; it is Hermitian in the general, complex case by definition of an inner product. 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 ...

  9. Semidefinite programming - Wikipedia

    en.wikipedia.org/wiki/Semidefinite_programming

    Semidefinite programming (SDP) is a subfield of mathematical programming concerned with the optimization of a linear objective function (a user-specified function that the user wants to minimize or maximize) over the intersection of the cone of positive semidefinite matrices with an affine space, i.e., a spectrahedron.