# Vector Space operations

1. Feb 13, 2005

### C0nfused

Hi everybody,
In vector spaces we define two operations, addition and scalar multiplication. Scalar multiplication is distributive over addition. This can define the order of operations in the vector space? I mean when we have an expression to calculate, we know that we firstly calculate multiplications and after that addition because of this fact? Or is it also a convention? Generally multiplication precedes addition and this also applies to expressions inside parentheses? (we also define that parentheses are calculated before anything else?)
Thanks

2. Feb 13, 2005

### jcsd

In a vector space a(B+C) you ould eiher calculate the vector B+C first and multply it by the scalr a or due to the bistrubitive propety you could caculate the vector aB and aC first and add them together. Howvere this is only due to the distroibuitve property of scalr multplication, otherwise you would have to claulate what was in the brackets first.

3. Feb 13, 2005

### mathwonk

i think he means that if you try to dispense with parentheses, say in the exporession cv+w, you know to compute cv first and then add w, rather than computing v+w first and then multiplying by c.

yes, this is the same convention as in junior high school.