Search results
Results from the WOW.Com Content Network
Both vector addition and scalar multiplication are trivial. A basis for this vector space is the empty set, so that {0} is the 0-dimensional vector space over F. Every vector space over F contains a subspace isomorphic to this one. The zero vector space is conceptually different from the null space of a linear operator L, which is the kernel of L.
When the scalar field is the real numbers, the vector space is called a real vector space, and when the scalar field is the complex numbers, the vector space is called a complex vector space. [4] These two cases are the most common ones, but vector spaces with scalars in an arbitrary field F are also commonly considered.
The java.lang.Class [2] class is the basis of more advanced introspection. For instance, if it is desirable to determine the actual class of an object (rather than whether it is a member of a particular class), Object.getClass() and Class.getName() can be used:
The most vexing parse is a counterintuitive form of syntactic ambiguity resolution in the C++ programming language. In certain situations, the C++ grammar cannot distinguish between the creation of an object parameter and specification of a function's type. In those situations, the compiler is required to interpret the line as a function type ...
In functional analysis, an F-space is a vector space over the real or complex numbers together with a metric: such that Scalar multiplication in X {\displaystyle X} is continuous with respect to d {\displaystyle d} and the standard metric on R {\displaystyle \mathbb {R} } or C . {\displaystyle \mathbb {C} .}
Let F be a field and let X be any set. The functions X → F can be given the structure of a vector space over F where the operations are defined pointwise, that is, for any f, g : X → F, any x in X, and any c in F, define (+) = + () = When the domain X has additional structure, one might consider instead the subset (or subspace) of all such functions which respect that structure.
Virtual inheritance ensures that only one instance of a base class exists in the inheritance graph, avoiding some of the ambiguity problems of multiple inheritance. Multiple inheritance is a C++ feature allowing a class to be derived from more than one base class; this allows for more elaborate inheritance relationships. For example, a "Flying ...
One common property of all sequential containers is that the elements can be accessed sequentially. Like all other standard library components, they reside in namespace std. The following containers are defined in the current revision of the C++ standard: array, vector, list, forward_list, deque.