Properties of dot product - proof, Mathematics

Assignment Help:

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.


Related Discussions:- Properties of dot product - proof

Matrix equation , Hi may i know how to substract the (ID)colum matrix from ...

Hi may i know how to substract the (ID)colum matrix from (K)square matrix as per equation below. E = (K - ID)^-1 S K is m*m matrix I is idntity matrix d is column vector s is col

Daily Math, Six times as many people voted in the 2012 election as in the 2...

Six times as many people voted in the 2012 election as in the 2008 election.If 162 people voted in 2008,how many people voted in both elections?

Variation of parameters, In this case we will require deriving a new formul...

In this case we will require deriving a new formula for variation of parameters for systems.  The derivation now will be much simpler than the when we first noticed variation of pa

Process for solving linear equations, 1. If the equation has any fractions ...

1. If the equation has any fractions employ the least common denominator to apparent the fractions. We will do this through multiplying both sides of the equation by the LCD. Al

Square and square root., the value of square root of 200multiplied by squar...

the value of square root of 200multiplied by square root of 5=

Example of hcf, Example  Find the Highest Common Factor of 54, 72...

Example  Find the Highest Common Factor of 54, 72 and 150. First we consider 54 and 72. The HCF for these two quantities is calculated as follows:

Mss. Ann, I need marketing management sample assignment as a guide

I need marketing management sample assignment as a guide

Explain adding rational expressions different denominators, Explain Adding ...

Explain Adding Rational Expressions with Different Denominators When you add or subtract fractions or rational expressions that have different denominators, you must first find

Determine the measure of the vertex angle, Determine the measure of the ver...

Determine the measure of the vertex angle of the isosceles triangle. a. 34° b. 16° c. 58° d. 112° d. Simply substitute x = 34 into the equation for the vertex angle,

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd