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An array type is a reference type that refers to a space containing one or more elements of a certain type. All array types derive from a common base class, System. Array. Each element is referenced by its index just like in C++ and Java. An array in C# is what would be called a dynamic array in C++.
Initialized does not mean correct if the value is a default one. (However, default initialization to 0 is a right practice for pointers and arrays of pointers, since it makes them invalid before they are actually initialized to their correct value.) In C, variables with static storage duration that are not initialized explicitly are initialized ...
For a tensor field of order k > 1, the tensor field of order k is defined by the recursive relation = where is an arbitrary constant vector. A tensor field of order greater than one may be decomposed into a sum of outer products, and then the following identity may be used: = ().
A property, in some object-oriented programming languages, is a special sort of class member, intermediate in functionality between a field (or data member) and a method.The syntax for reading and writing of properties is like for fields, but property reads and writes are (usually) translated to 'getter' and 'setter' method calls.
The name "field with one element" and the notation F 1 are only suggestive, as there is no field with one element in classical abstract algebra. Instead, F 1 refers to the idea that there should be a way to replace sets and operations, the traditional building blocks for abstract algebra, with other, more flexible objects.
The flow field around an airplane is a vector field in R 3, here visualized by bubbles that follow the streamlines showing a wingtip vortex. Vector fields are commonly used to create patterns in computer graphics. Here: abstract composition of curves following a vector field generated with OpenSimplex noise.
A bivector is an oriented plane element and a trivector is an oriented volume element, in the same way that a vector is an oriented line element. Given vectors a, b and c, the product is a trivector with magnitude equal to the scalar triple product, i.e.
The complex numbers are usually identified with the coordinate axes and two-dimensional vectors, which would mean associating them with the vector elements of the geometric algebra. There is no contradiction in this, as to get from a general vector to a complex number an axis needs to be identified as the real axis, e 1 say. This multiplies by ...