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Therefore, both Java and C# treat array types covariantly. For instance, in Java String [] is a subtype of Object [], and in C# string [] is a subtype of object []. As discussed above, covariant arrays lead to problems with writes into the array. Java [4]: 126 and C# deal with this by marking each array object with a type when it is created ...
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.
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 ...
Probably the most commercially important recent object-oriented languages are Java, developed by Sun Microsystems, as well as C# and Visual Basic.NET (VB.NET), both designed for Microsoft's .NET platform. Each of these two frameworks shows, in its way, the benefit of using OOP by creating an abstraction from implementation.
In array languages, operations are generalized to apply to both scalars and arrays. Thus, a+b expresses the sum of two scalars if a and b are scalars, or the sum of two arrays if they are arrays. An array language simplifies programming but possibly at a cost known as the abstraction penalty.
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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]
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