Properties of dot product - proof, Mathematics

Properties of Dot Product - proof

Proof of: If v v = 0 then v = 0

This is a pretty simple proof.  Let us start with v = (v1 , v2 ,.... , vn) and compute the dot product.

 v • v = (v1,v2,..., vn) • (v1,v2,....,vn)

= v21, v22 +.... + v2n

 = 0

Now, since we know v2i ≥ 0 for all i then the only way for this sum to be zero is to in fact have v2i = 0. This in turn however means that we must have vi = 0 and so we must have had v = 0.

Posted Date: 4/13/2013 2:22:45 AM | Location : United States

Related Discussions:- Properties of dot product - proof, Assignment Help, Ask Question on Properties of dot product - proof, Get Answer, Expert's Help, Properties of dot product - proof Discussions

Write discussion on Properties of dot product - proof
Your posts are moderated
Related Questions
If the following terms form a AP. Find the common difference & write the next 3 terms3, 3+ √2, 3+2√2, 3+3√2.......... Ans:    d= √2 next three terms 3 + 4 √ 2 , 3 + 5√ 2 ,

Company A and Company B have spent a lot of money on research to develop a cure for the common cold. Winter is approaching and there is certainly going to be a lot of demand for th

Is the group of order 10 simple?

For this point we've only looked as solving particular differential equations. Though, many "real life" situations are governed through a system of differential equations. See the

A firm buys a product using the price schedule given in the table: The company estimate holding costs at 10% of the purchase price per year and ordering costs at $40 per order .

Consider the equation x 2 y′′+ xy′- y = 4x ln x (a) Verify that x is a solution to the homogeneous equation. (b) Use the method of reduction of order to derive the second

Audrey is creating a increased flowerbed which is 4.5 ft by 4.5 ft. She requires computing how much lumber to buy. If she requires knowing the distance around the flowerbed, which