The definition of a vector as being something that has 'magnitude' and 'direction' is actually incorrect. If that were to be the case, a quantity like electric current would be a vector and not a scalar. Electric current is a scalar.
A vector is something that transforms like the coordinate system, while a scalar does not. In other words, if you were to transform the coordinate system by a certain operator, a vector quantity in the old coordinate system can be transformed into the new one by using exactly the same operator. This is the correct definition of a vector. G. On Thu, 14 Oct 2010 10:22:59 -0400, Ed Pozharski <epozh...@umaryland.edu> wrote: > The definition game is on! :) > > Vectors are supposed to have direction and amplitude, unlike scalars. > Curiously, one can take a position that real numbers are vectors too, if > you consider negative and positive numbers having opposite directions > (and thus subtraction is simply a case of addition of a negative > number). And of course, both scalars and vectors are simply tensors, of > zeroth and first order :) > > Guess my point is that definitions are a matter of choice in math and if > vector is defined as an array which must obey addition and scaling rules > (but there is no fixed multiplication rule - regular 3D vectors have > more than one possible product), then complex numbers are vectors. In a > narrow sense of a real space vectors (the arrow thingy) they are not. > Thus, complex number is a Vector, but not the vector (futile attempt at > using articles by someone organically suffering from article dyslexia). > > Cheers, > > Ed. > > > O -- ********************************************** Blow, blow, thou winter wind Thou art not so unkind As man's ingratitude; Thy tooth is not so keen, Because thou art not seen, Although thy breath be rude. -William Shakespeare **********************************************
