This site is devoted to mathematics and its applications. Created and run by Peter Saveliev.

# Vector space

From Mathematics Is A Science

Jump to navigationJump to searchThere are two operations: addition of two vectors and multiplication of a vector by a scalar. The satisfy the following axioms:

- X+Y=Y+X for all X and Y
- X+(Y+Z)=(X+Y)+Z for all X, Y, and Z
- X+0=X=0+X for some element 0 in V and all X
- X+(-X)=0 for any X and some element -X in V
- a(bX)=(ab)X for all X and all scalars a, b
- 1X=X for all X
- a(X+Y)=aX+aY for all X and Y
- (a+b)X=aX+bX for all X, Y and all scalars a, b

See also Vectors.