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Common examples of array slicing are extracting a substring from a string of characters, the "ell" in "hello", extracting a row or column from a two-dimensional array, or extracting a vector from a matrix. Depending on the programming language, an array slice can be made out of non-consecutive elements.
Matrix representation is a method used by a computer language to store column-vector matrices of more than one dimension in memory. Fortran and C use different schemes for their native arrays. Fortran uses "Column Major" ( AoS ), in which all the elements for a given column are stored contiguously in memory.
For example, for the 2×2 matrix = [], the half-vectorization is = []. There exist unique matrices transforming the half-vectorization of a matrix to its vectorization and vice versa called, respectively, the duplication matrix and the elimination matrix .
The Nial example of the inner product of two arrays can be implemented using the native matrix multiplication operator. If a is a row vector of size [1 n] and b is a corresponding column vector of size [n 1]. a * b; By contrast, the entrywise product is implemented as: a .* b;
Some compiled languages such as Ada and Fortran, and some scripting languages such as IDL, MATLAB, and S-Lang, have native support for vectorized operations on arrays. For example, to perform an element by element sum of two arrays, a and b to produce a third c, it is only necessary to write c = a + b
In linear algebra, a column vector with elements is an matrix [1] consisting of a single column of entries, for example, = [].. Similarly, a row vector is a matrix for some , consisting of a single row of entries, = […]. (Throughout this article, boldface is used for both row and column vectors.)
A matrix with the same number of rows and columns is called a square matrix. [5] A matrix with an infinite number of rows or columns (or both) is called an infinite matrix. In some contexts, such as computer algebra programs, it is useful to consider a matrix with no rows or no columns, called an empty matrix.
For example, if V is an m × n matrix, W is an m × p matrix, and H is a p × n matrix then p can be significantly less than both m and n. Here is an example based on a text-mining application: Let the input matrix (the matrix to be factored) be V with 10000 rows and 500 columns where words are in rows and documents are in columns.