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In mathematics, brackets of various typographical forms, such as parentheses ( ), square brackets [ ], braces { } and angle brackets , are frequently used in mathematical notation. Generally, such bracketing denotes some form of grouping: in evaluating an expression containing a bracketed sub-expression, the operators in the sub-expression take ...
In mathematical physics, especially quantum mechanics, it is common to write the inner product between elements as a|b , as a short version of a| · |b , or a| Ô |b , where Ô is an operator. This is known as Dirac notation or bra–ket notation, to note vectors from the dual spaces of the Bra A| and the Ket |B .
Brackets: Angle bracket, Parenthesis • Bullet: Interpunct ‸ ⁁ ⎀ Caret (proofreading) Caret (computing) (^) Chevron (non-Unicode name) Caret, Circumflex, Guillemet, Hacek, Glossary of mathematical symbols ^ Circumflex (symbol) Caret (The freestanding circumflex symbol is known as a caret in computing and mathematics)
In the United Kingdom and many other English-speaking countries, "brackets" means (), known in the US as "parentheses" (singular "parenthesis"). That said, the specific terms "parentheses" and "square brackets" are generally understood everywhere and may be used to avoid ambiguity. The symbol of grouping knows as "braces" has two major uses.
A few letters, such as that of the voiced pharyngeal fricative, ʕ , were inspired by other writing systems (in this case, the Arabic letter ﻉ , ʿayn, via the reversed apostrophe). [9] Some letter forms derive from existing letters: The right-swinging tail, as in ʈ ɖ ɳ ɽ ʂ ʐ ɻ ɭ , indicates retroflex articulation.
However, where one or more sentences are wholly inside brackets, place their punctuation inside the brackets. There should be no space next to the inner side of a bracket. An opening bracket should usually be preceded by a space. This may not be the case if it is preceded by an opening quotation mark, another opening bracket, or a portion of a ...
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The inner product of two vectors (also known as the scalar product, not to be confused with scalar multiplication) is represented as an ordered pair enclosed in angle brackets. The inner product of two vectors u and v would be represented as: u , v {\displaystyle \langle \mathbf {u} ,\mathbf {v} \rangle }