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As exchanging the indices of an array is the essence of array transposition, an array stored as row-major but read as column-major (or vice versa) will appear transposed. As actually performing this rearrangement in memory is typically an expensive operation, some systems provide options to specify individual matrices as being stored transposed.
OFFT - recursive block in-place transpose of square matrices, in Fortran; Jason Stratos Papadopoulos, blocked in-place transpose of square matrices, in C, sci.math.num-analysis newsgroup (April 7, 1998). See "Source code" links in the references section above, for additional code to perform in-place transposes of both square and non-square ...
For "one-dimensional" (single-indexed) arrays – vectors, sequence, strings etc. – the most common slicing operation is extraction of zero or more consecutive elements. Thus, if we have a vector containing elements (2, 5, 7, 3, 8, 6, 4, 1), and we want to create an array slice from the 3rd to the 6th items, we get (7, 3, 8, 6).
In addition to support for vectorized arithmetic and relational operations, these languages also vectorize common mathematical functions such as sine. For example, if x is an array, then y = sin (x) will result in an array y whose elements are sine of the corresponding elements of the array x. Vectorized index operations are also supported.
Indexes are also called subscripts. An index maps the array value to a stored object. There are three ways in which the elements of an array can be indexed: 0 (zero-based indexing) The first element of the array is indexed by subscript of 0. [8] 1 (one-based indexing) The first element of the array is indexed by subscript of 1. n (n-based indexing)
In linear algebra, the transpose of a matrix is an operator which flips a matrix over its diagonal; that is, it switches the row and column indices of the matrix A by producing another matrix, often denoted by A T (among other notations). [1] The transpose of a matrix was introduced in 1858 by the British mathematician Arthur Cayley. [2]
However, a language wishing to index arrays from 1 could adopt the convention that every array address is represented by a′ = a – s; that is, rather than using the address of the first array element, such a language would use the address of a fictitious element located immediately before the first actual element. The indexing expression for ...
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]