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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.
In mathematics, positive semidefinite may refer to: Positive semidefinite function; Positive semidefinite matrix; Positive semidefinite quadratic form;
Circumflex (symbol) Caret (The freestanding circumflex symbol is known as a caret in computing and mathematics) Circumflex (diacritic), Caret (computing), Hat operator ̂: Circumflex (diacritic) Grave, Tilde: Combining Diacritical Marks, Diacritic: Colon: Semicolon, Comma: Cedilla, Decimal separator ⁒ Commercial minus sign: Minus sign ...
In logic, a set of symbols is commonly used to express logical representation. The following table lists many common symbols, together with their name, how they should be read out loud, and the related field of mathematics.
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 .
The symbol is definitely not my invention — it appeared in popular magazines (not mathematical ones) before I adopted it, but, once again, I seem to have introduced it into mathematics. It is the symbol that sometimes looks like , and is used to indicate an end, usually the end of a proof.
Suppose a vector norm ‖ ‖ on and a vector norm ‖ ‖ on are given. Any matrix A induces a linear operator from to with respect to the standard basis, and one defines the corresponding induced norm or operator norm or subordinate norm on the space of all matrices as follows: ‖ ‖, = {‖ ‖: ‖ ‖ =} = {‖ ‖ ‖ ‖:} . where denotes the supremum.
One can define positive-definite functions on any locally compact abelian topological group; Bochner's theorem extends to this context. Positive-definite functions on groups occur naturally in the representation theory of groups on Hilbert spaces (i.e. the theory of unitary representations).