Fundamentals of Statistics contains material of various lectures and courses of H. Lohninger on statistics, data analysis and chemometrics......click here for more.

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).

Vector addition 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:

  • 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 (ak) + (xk) = (yk) 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)

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

Last Update: 2012-10-08