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

Shares and dividend, A man in rested rupee 800 is buying rupee5 shares and ...

A man in rested rupee 800 is buying rupee5 shares and then they are selling at premium of rupee 1.15.he sells all the share.find profit?

Introduction to why learn mathematics, INTRODUCTION : All of us have encou...

INTRODUCTION : All of us have encountered mathematics while growing up. Some of us have grown to like it, and therefore, enjoy. doing it. Some others have developed a lukewarm rel

Alegbra, what iz the value of x if y=56

what iz the value of x if y=56

Basic mathematics, I need help with my homework, I am to the edge right now...

I need help with my homework, I am to the edge right now with this w=5pq/2

Decimal representations of some basic angles, Decimal representations of so...

Decimal representations of some basic angles: As a last quick topic let's note that it will, on occasion, be useful to remember the decimal representations of some basic angles. S

Determinant of an n×n matrix, How can we calculate the Determinant of an N×...

How can we calculate the Determinant of an N×N Matrix?

Draw a common graph f ( x ) = |x|, Graph f ( x ) = |x| Solution The...

Graph f ( x ) = |x| Solution There actually isn't much to in this problem outside of reminding ourselves of what absolute value is. Remember again that the absolute value f

Managment Science, Classify models based on the degree of their abstraction...

Classify models based on the degree of their abstraction, and provide some examples of such models.

Plane figures, what are the formulas for finding the area and volume of pla...

what are the formulas for finding the area and volume of plane figures

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