>Then you're using a definition of vector, not used in any mathematics course. [...] A vector is by definition no more and no less than an element of a vector space.
It's the definition I was given. If you accept that the word "vector" may be given a definition different from the one you give it, you'll need to concede that an std::vector may be a vector.
>you don't choose them. You choose the field and dimension, and those operations (vector addition and scalar multiplication) are a consequence.
You're using the phrase "vector addition and scalar multiplication" in a different sense than I meant. I was referring to component-wise addition between two vectors and to multiplication between a scalar and the individual components of a vector. You could choose different operations to construct a vector space, as long as they meet the requirements of vector spaces.
You used the phrase to refer to the constructing operations of a vector space. So yes, a vector space is indeed constructed out of the operations it is constructed out of. You could have been more charitable in your interpretation of my words, rather than assume I was saying something equivalent to "four-cornered triangle".
It's the definition I was given. If you accept that the word "vector" may be given a definition different from the one you give it, you'll need to concede that an std::vector may be a vector.
>you don't choose them. You choose the field and dimension, and those operations (vector addition and scalar multiplication) are a consequence.
You're using the phrase "vector addition and scalar multiplication" in a different sense than I meant. I was referring to component-wise addition between two vectors and to multiplication between a scalar and the individual components of a vector. You could choose different operations to construct a vector space, as long as they meet the requirements of vector spaces.
You used the phrase to refer to the constructing operations of a vector space. So yes, a vector space is indeed constructed out of the operations it is constructed out of. You could have been more charitable in your interpretation of my words, rather than assume I was saying something equivalent to "four-cornered triangle".