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Deutsch: Dieses Dokument listet 20323 Symbole und die dazugehörigen LaTeX-Befehle auf. Manche Symbole sind in jedem LaTeX-2ε-System verfügbar; andere benötigen zusätzliche Schriftarten oder Pakete, die nicht notwendig in jeder Distribution mitgeliefert werden und daher selbst installiert werden müssen.
Print/export Download as PDF; Printable version; In other projects ... In mathematics, positive semidefinite may refer to: Positive semidefinite function ...
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 .
According to that sign, the quadratic form is called positive-definite or negative-definite. A semidefinite (or semi-definite) quadratic form is defined in much the same way, except that "always positive" and "always negative" are replaced by "never negative" and "never positive", respectively.
Print/export Download as PDF; Printable version; In other projects ... as Q is positive semidefinite and the non-negativity constraints form a convex feasible set. [7]
If A has only real entries, then A T A is a positive-semidefinite matrix. = (). The transpose of an invertible matrix is also invertible, and its inverse is the transpose of the inverse of the original matrix.
If the quadratic form f yields only non-negative values (positive or zero), the symmetric matrix is called positive-semidefinite (or if only non-positive values, then negative-semidefinite); hence the matrix is indefinite precisely when it is neither positive-semidefinite nor negative-semidefinite. A symmetric matrix is positive-definite if and ...
The Hessian matrix is commonly used for expressing image processing operators in image processing and computer vision (see the Laplacian of Gaussian (LoG) blob detector, the determinant of Hessian (DoH) blob detector and scale space). It can be used in normal mode analysis to calculate the different molecular frequencies in infrared ...