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Printable version; In other projects Wikidata item; Appearance. move to sidebar hide. In mathematics, positive semidefinite may refer to: Positive semidefinite ...
Less-than sign: Angle bracket, Chevron, Guillemet Lozenge: Square lozenge ("Pillow") ☞ Manicule: Index, Obelus: º: Masculine ordinal indicator: Feminine ordinal indicator, Degree sign: −: Minus sign: Hyphen-minus, Commercial minus: ×: Multiplication sign: X mark # Number sign: Numero sign. Also known as "octothorpe", "hash" and "hashtag ...
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 .
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.
1. Denotes either a plus sign or a minus sign. 2. Denotes the range of values that a measured quantity may have; for example, 10 ± 2 denotes an unknown value that lies between 8 and 12. ∓ (minus-plus sign) Used paired with ±, denotes the opposite sign; that is, + if ± is –, and – if ± is +. ÷ (division sign)
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.
The off-diagonal elements are complex conjugates of each other (also called coherences); they are restricted in magnitude by the requirement that () be a positive semi-definite operator, see below. A density operator is a positive semi-definite , self-adjoint operator of trace one acting on the Hilbert space of the system.
A form is called strongly positive if it is a linear combination of products of semi-positive forms, with positive real coefficients. A real (p, p) -form η {\displaystyle \eta } on an n -dimensional complex manifold M is called weakly positive if for all strongly positive (n-p, n-p) -forms ζ with compact support, we have ∫ M η ∧ ζ ≥ 0 ...