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A vector treated as an array of numbers by writing as a row vector or column vector (whichever is used depends on convenience or context): = (), = Index notation allows indication of the elements of the array by simply writing a i, where the index i is known to run from 1 to n, because of n-dimensions. [1]
This allows MathJax to run in any browser with JavaScript support, including mobile devices. [17] MathJax can display math by using a combination of HTML and CSS or by using the browser's native MathML support, when available. The exact method MathJax uses to typeset math is determined by the capabilities of the user's browser, fonts available ...
General array slicing can be implemented (whether or not built into the language) by referencing every array through a dope vector or descriptor – a record that contains the address of the first array element, and then the range of each index and the corresponding coefficient in the indexing formula.
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
The vector maintains a certain order of its elements, so that when a new element is inserted at the beginning or in the middle of the vector, subsequent elements are moved backwards in terms of their assignment operator or copy constructor. Consequently, references and iterators to elements after the insertion point become invalidated.
Here, c[i:i+3] represents the four array elements from c[i] to c[i+3] and the vector processor can perform four operations for a single vector instruction. Since the four vector operations complete in roughly the same time as one scalar instruction, the vector approach can run up to four times faster than the original code.
The transpose (indicated by T) of any row vector is a column vector, and the transpose of any column vector is a row vector: […] = [] and [] = […]. The set of all row vectors with n entries in a given field (such as the real numbers ) forms an n -dimensional vector space ; similarly, the set of all column vectors with m entries forms an m ...
A property, in some object-oriented programming languages, is a special sort of class member, intermediate in functionality between a field (or data member) and a method.The syntax for reading and writing of properties is like for fields, but property reads and writes are (usually) translated to 'getter' and 'setter' method calls.