Question

what are binary operations in vector space

Answer 1

A binary operation is an operation that takes two variables and outputs a result. It's something like f(x,y) =

It takes two inputs and gives 1 output.

Answer 2

addition of 2 vectors, dot product...

Answer 3

Well a vector space doesn't have to be literal vectors, does it?

Answer 4

if we need to prove that r is a vector space.for this all the binary operations should be done

Answer 5

Ah, the axioms....

Answer 6

to show that r is vector space .what exactly to be done

Answer 7

Show that two vectors can be added together. In other words, show that addition is a binary operation.
Show that a vector can be multiplies by a scalar.

Answer 8

Oh nevermind. I found the axioms.
http://en.wikipedia.org/wiki/Vector_space#Definition

Answer 9

Yeah okay. So they are going to give you a set of things and then 2 binary operations, calling 1 addition and the other multiplication. They may or may not be like regular addition and mult. You then have to prove those 8 axioms.

Answer 10

if c=(a,b)= where f is a continous function.show that v is a vector space over r.first ao all what is a continous function

Answer 11

You had probably better ask that as a new question....

Answer 12

A continuous function? Intuitively? Or as a formal definition?

Answer 13

for r in vector space it is (x),for r2 it is (x,y), in vector space then what should be for rN .should be it proven in same method as that for other vector spaces.

Answer 14

Intuitively, it just means that the function doesn't have any "breaks" or "jumps."
If f(x) is 1 and f(x+1) =2, then the function hits every value between the two.