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In many languages (such as C), one should specify the number of elements contained in the array; whereas in others (such as Pascal and Visual Basic .NET) one should specify the numeric value of the index of the last element. Needless to say, this distinction is immaterial in languages where the indices start at 1, such as Lua.
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]
even = x (2:: 2); odd = x (:: 2); is how one would use Fortran to create arrays from the even and odd entries of an array. Another common use of vectorized indices is a filtering operation.
The first element of the array is indexed by subscript of 1. n (n-based indexing) The base index of an array can be freely chosen. Usually programming languages allowing n-based indexing also allow negative index values and other scalar data types like enumerations, or characters may be used as an array index.
Zero-based numbering is a way of numbering in which the initial element of a sequence is assigned the index 0, rather than the index 1 as is typical in everyday non-mathematical or non-programming circumstances.
An n-by-n matrix A is an anti-diagonal matrix if the (i, j) th element a ij is zero for all rows i and columns j whose indices do not sum to n + 1. Symbolically: a i j = 0 ∀ i , j ∈ { 1 , … , n } , ( i + j ≠ n + 1 ) . {\displaystyle a_{ij}=0\ \forall i,j\in \left\{1,\ldots ,n\right\},\ (i+j\neq n+1).}
the Greek alphabet is used for space and time components, where indices take on values 0, 1, 2, or 3 (frequently used letters are μ, ν, ... the Latin alphabet is used for spatial components only, where indices take on values 1, 2, or 3 (frequently used letters are i , j , ...
A (0,0) tensor is a number in the field . A (1,0) tensor is a vector. A (0,1) tensor is a covector. A (0,2) tensor is a bilinear form. An example is the metric tensor . A (1,1) tensor is a linear map.