Intro_14_01.m

% 20130515 XY511 09:00 
% AbrahamX @ NWPU

u = [10, -11, 12];
v = [20; -21; -22];
prod = u * v

w = [2, 1, 3];
z = [7; 6; 5]
% u * w








% Comment: We shall describe two ways in which a meaning may be
% attributed to the product of two vectors. In both cases the vectors
% concerned must have the same length.

% The first product is the standard scalar product. Suppose that u 
% and v are two vectors of length n, u being a row vector and v a column
% vector. The scalar product is defined by multiplying the corresponding
% elements together and adding the results to a given single number
% (scalar).

% The second way of forming the product of two vectors of the same length
% is known as the Hadamard product. It is not often usd in Mathematics but
% is an invaluable MATLAB feature. It involves vectors of the same type. If
% u and v are two vectors of the same type (both row vectors or both column
% vectors), the mathematical definition of this product, which we shall
% call the [dot product], is the VECTOR having the components u*v = [u1v1, 
% u2v2, ..., unvn].------->The result is a vector of the same length and
% type as u and v. Thus, we simply multiply the corresponding elements of
% two vectors.