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

Matrices, what are eigen values

what are eigen values

How i get orders, how i become an assignment helper?n how i get order from ...

how i become an assignment helper?n how i get order from students?what should i do

Multiplication in decimal notations., Consider the following multiplication...

Consider the following multiplication in decimal notations: (999).(abc)=def132 ,determine the digits a,b,c,d,e,f. solution) a=8 b=6 c=8 d=8 e=6 f=7 In other words, 999 * 877 = 8

Devision, how many times can u put 10000 into 999999

how many times can u put 10000 into 999999

Why x and y are simplifying expressions, Why x and y are Simplifying Expres...

Why x and y are Simplifying Expressions? You're doing algebra now, and you know you're going to see x's and y's. But before we work with x's and y's, we'll explore why we use t

Random variable, RANDOM VARIABLE A variable which assumes differ...

RANDOM VARIABLE A variable which assumes different numerical values as a result of random experiments or random occurrences is known as a random variable. The rainfal

Solid mensuration, what is the importance of solid mensuration?

what is the importance of solid mensuration?

Quantitative Techniques, You are given that the total frequency is 900 and ...

You are given that the total frequency is 900 and the median 100.48. From the following frequency distribution, find the class frequencies that are missing. Intelligence No. of Int

Trigonometry, Show that the radius of the circle,passing through the centre...

Show that the radius of the circle,passing through the centre of the inscribed circle of a triangle and any two of the centres of the escribed circles,is equal to the diameter of t

Example of problems related to applying operations, I had just come back fr...

I had just come back from a very interesting talk arranged by a Mathematics Centre, it was aimed at parents of primary school-going children. They had talked about, and demonstrate

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