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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: ck:=ak+bk
There are several rules for the addition of vectors:
 
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-Jšn-18