All formulas of mathematical vectors

1, vector addition

Algorithm of vector addition;

Commutation law: a+b = b+a.

Law of association: (a+b)+c=a+(b+c).

2. Vector subtraction

If A and B are mutually opposite vectors, then the reciprocal of a =-b, b =-a and a+b = 0.0 is 0.

AB-AC=CB。 That is, "common starting point, decreasing direction".

A=(x, y) b=(x', y') Then a-b=(x-x', y-y').

4. Multiply the number by the vector

Distribution law of vector logarithm (first distribution law): (λ+μ) a = λ a+μ a.

The distribution law of number pair vector (second distribution law): λ (a+b) = λ a+λ b.

related notion

The concept of geometric vector is abstracted from linear algebra to get a more general concept of vector. Here, a vector is defined as an element of a vector space. It should be noted that these abstract vectors are not necessarily represented by number pairs, and the concepts of size and direction are not necessarily applicable.

Therefore, when reading on weekdays, it is necessary to distinguish what kind of concept "vector" is in the text according to the context. However, we can still find the basis of a vector space to set the coordinate system, and we can also define the norm and inner product on the vector space by choosing a suitable definition, which enables us to compare abstract vectors with specific geometric vectors.