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In numerical analysis and scientific computing, a sparse matrix or sparse array is a matrix in which most of the elements are zero. [1] There is no strict definition regarding the proportion of zero-value elements for a matrix to qualify as sparse but a common criterion is that the number of non-zero elements is roughly equal to the number of ...
In these three, sequence types (C arrays, Java arrays and lists, and Lisp lists and vectors) are indexed beginning with the zero subscript. Particularly in C, where arrays are closely tied to pointer arithmetic, this makes for a simpler implementation: the subscript refers to an offset from the starting position of an array, so the first ...
A square matrix containing zeros in all entries except for the first row, first column, and main diagonal. Band matrix: A square matrix whose non-zero entries are confined to a diagonal band. Bidiagonal matrix: A matrix with elements only on the main diagonal and either the superdiagonal or subdiagonal. Sometimes defined differently, see article.
Zero-forcing (or null-steering) precoding is a method of spatial signal processing by which a multiple antenna transmitter can null the multiuser interference in a multi-user MIMO wireless communication system. [1]
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. Consider a clipping operation of a sine wave where amplitudes larger than 0.5 are to be set to 0.5. Using S-Lang, this can be done by
Each number in the input array A could be positive, negative, or zero. [1] For example, for the array of values [−2, 1, −3, 4, −1, 2, 1, −5, 4], the contiguous subarray with the largest sum is [4, −1, 2, 1], with sum 6. Some properties of this problem are: If the array contains all non-negative numbers, then the problem is trivial; a ...
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).}
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).