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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)

or:

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.

or:

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.

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    Why would you want to *not* distinguish the two in your program? It seems to me that it would be extra work to have to convert the result to a vector, every time a computation returns a column matrix. In addition, the distinction can make it easier to pinpoint mistakes, like type checking in programming languages.2015-01-19

3 Answers 3