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NumPy (pronounced / ˈ n ʌ m p aɪ / NUM-py) is a library for the Python programming language, adding support for large, multi-dimensional arrays and matrices, along with a large collection of high-level mathematical functions to operate on these arrays. [3]
Formally, a parity check matrix H of a linear code C is a generator matrix of the dual code, C ⊥. This means that a codeword c is in C if and only if the matrix-vector product Hc ⊤ = 0 (some authors [1] would write this in an equivalent form, cH ⊤ = 0.) The rows of a parity check matrix are the coefficients of the parity check equations. [2]
An array data structure can be mathematically modeled as an abstract data structure (an abstract array) with two operations get(A, I): the data stored in the element of the array A whose indices are the integer tuple I. set(A, I, V): the array that results by setting the value of that element to V. These operations are required to satisfy the ...
Function rank is an important concept to array programming languages in general, by analogy to tensor rank in mathematics: functions that operate on data may be classified by the number of dimensions they act on. Ordinary multiplication, for example, is a scalar ranked function because it operates on zero-dimensional data (individual numbers).
SymPy is an open-source Python library for symbolic computation.It provides computer algebra capabilities either as a standalone application, as a library to other applications, or live on the web as SymPy Live [2] or SymPy Gamma. [3]
Thus a one-dimensional array is a list of data, a two-dimensional array is a rectangle of data, [12] a three-dimensional array a block of data, etc. This should not be confused with the dimension of the set of all matrices with a given domain, that is, the number of elements in the array.
Their number of elements is necessarily of the form p n where p is a prime number and n is a positive integer, and two finite fields of the same size are isomorphic. The prime p is called the characteristic of the field, and the positive integer n is called the dimension of the field over its prime field .
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.