Addition of Vectors

Addition of vectors is only defined concerning vectors with the same type of elements and the same form (row or column) and order (number of elements in a vector).
 

Definition

Let a, b, and c be vectors of the same order and form. The sum c := a+b  is then calculated by adding up the corresponding elements of the vectors a and b: c_k:=a_k+b_k

• the commutative law: a+b = b+a
• the associative law: (a+b)+c = a+(b+c)
• and the law that the solution x of the equation (a_k) + (x_k) = (y_k) is unique to the given vectors a and y

Examples

(1.4, 4.2, 0, -1.2, 2.3) + (0, 0, 0, 0, 0) = (1.4, 4.2, 0, -1.2, 2.3)

1 4 5 -1 0

+

-1 -4 -5 1 0

=

0 0 0 0 0

 

(1.2,3.3,-3.2) + (1,-3) cannot be added