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Table of Contents Math Background Vectors Addition of Vectors	Index
See also: subtraction of vectors, addition of matrices

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

Last Update: 2006-Jän-18