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When the direction of a Euclidean vector is represented by an angle , this is the angle determined by the free vector (starting at the origin) and the positive -unit vector. The same concept may also be applied to lines in a Euclidean space, where the angle is that determined by a parallel to the given line through the origin and the positive x ...
CTAN (an acronym for "Comprehensive TeX Archive Network") is the authoritative place where TeX-related material and software can be found for download. Repositories for other projects, such as the MiKTeX distribution of TeX, constantly mirror most of CTAN.
After a short configuration process and mirror selection, it uses tools available on the user's computer to automatically download, unpack, compile, test, and install modules. It can also self-update. An effort to replace CPAN.pm with something cleaner and more modern resulted in the CPANPLUS (or CPAN++) set of modules.
The third gives symbols listed elsewhere in the table that are similar to it in meaning or appearance, or that may be confused with it; The fourth (if present) links to the related article(s) or adds a clarification note.
The Oxford English Dictionary records the use of the word injection as a noun by S. Mac Lane in Bulletin of the American Mathematical Society (1950), and injective as an adjective by Eilenberg and Steenrod in Foundations of Algebraic Topology (1952). [6]
In mathematics, sine and cosine are trigonometric functions of an angle.The sine and cosine of an acute angle are defined in the context of a right triangle: for the specified angle, its sine is the ratio of the length of the side that is opposite that angle to the length of the longest side of the triangle (the hypotenuse), and the cosine is the ratio of the length of the adjacent leg to that ...
Sometimes, for the clarity of reading, different kinds of brackets are used to express the same meaning of precedence in a single expression with deep nesting of sub-expressions. [1] Historically, other notations, such as the vinculum, were similarly used for grouping. In present-day use, these notations all have specific meanings.
The exact definition of the term varies depending on the subfield (and sometimes even the author). In linear algebra , it is synonymous with a linear form , which is a linear mapping from a vector space V {\displaystyle V} into its field of scalars (that is, it is an element of the dual space V ∗ {\displaystyle V^{*}} ) [ 1 ]