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

What is equivalence relation, What is equivalence relation?  Prove that rel...

What is equivalence relation?  Prove that relation  'congruence modulo' (  ≡mod m) is an equivalence relation.  Ans: A relation R illustrated on a nonempty set A is said to be

Differential Equations, 1.Verify Liouville''s formula for y "-y" - y'' + y ...

1.Verify Liouville''s formula for y "-y" - y'' + y = 0 in (0, 1) ? 2.Find the normalized differential equation which has {x, xex} as its fundamental set. 3.6Find the general soluti

Differentiate quotient rule functions, Example of quotient rule : Let's no...

Example of quotient rule : Let's now see example on quotient rule.  In this, unlike the product rule examples, some of these functions will require the quotient rule to get the de

Trigonometry, Solve the following: Line Bearings Distance a...

Solve the following: Line Bearings Distance a. N 15 E 4km b. S 10 E ? c. N 80 W ?

Kotler, Marketing management,Analysis,planning and implementation

Marketing management,Analysis,planning and implementation

I want to learn mathematics, I was never really good at mathematics what is...

I was never really good at mathematics what is the best way? I am reading Math better explained but is there anything else I can do? I want to study advanced topics and get a good

If 967.234 is divided by 10 how will the decimal point move, If 967.234 is ...

If 967.234 is divided by 10, how will the decimal point move? It will move one place to the left. While dividing by multiples of 10, the decimal point is moved to the left acco

Find the area irrigated by this system, An irrigation system uses a straigh...

An irrigation system uses a straight 30m sprinkler pipe which is capped at one end and arranged so that all water is released directly downwards and pivots around a central point.

Determine the differential y = t 3 - 4t 2 + 7t, Determine the differentia...

Determine the differential for following.                                      y = t 3 - 4t 2 + 7t Solution Before working any of these we have to first discuss just

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