I'm writing a mathematical library; and I have an idea where I want to automatically turn column matrices and row matrices to vectors, with all of the mathematical properties of a vector.
Answer I'm looking for:
Someone with good mathematical reasoning explaining why:
column matrices, column vectors, row matrices, row vectors should not be treated as the same thing. (The library will ofcourse understand operations like [[1,2],[3,4]] * [1,2], where [1,2] is a vector)
some kind of showcase or example where it is impossible for a library that can't differentiate between row vectors and column vectors to know which one of several possible answers are correct.
some kind of evidence that it is in fact possible to do this.
please note: inner vector multiplication will be easily integrated by using a special function for that function rather than the * sign.