Why is a C++ Vector called a Vector?

Question

The question\'s pretty self-explanatory really. I know vaguely about vectors in maths, but I don\'t really see the link to C++ vectors.

Answer 1

It is just the name. C++ vector could very well (or maybe even more accurate) be called dynamic array or resizable array but this name was simply chosen. This vector is not the same as vector from methematics because in mathematics vectors are members of any set V such that there are two important operations defined on this set: + (addition of vectors) and x (multiplication of a vector by a scalar from field F) and these operations satisfy 8 axioms:

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Associativity of addition

u + (v + w) = (u + v) + w

Commutativity of addition

u + v = v + u

Identity element of addition

There exists an element 0 ∈ V, called the zero vector, such that v + 0 = v for all v ∈ V.

Inverse elements of addition

For every v ∈ V, there exists an element −v ∈ V, called the additive inverse of v, such that v + (−v) = 0

Compatibility of scalar multiplication with field multiplication

a(bv) = (ab)v

Identity element of scalar multiplication

1 v = v, where 1 denotes the multiplicative identity in F.

Distributivity of scalar multiplication with respect to vector addition  

a(u + v) = au + av

Distributivity of scalar multiplication with respect to field addition

(a + b)v = av + bv

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C++ std::vector supports all of them (not directly, but via C++ features), so it can somehow be called a vector, but it is just colloquialism and for example Vallaray pointed out by Bjarne Stroustrup in "C++ Programming Language" supports some of them directly.