Purchase Solution

Inequality: Proof using Unit Vectors

Not what you're looking for?

Ask Custom Question

Prove that (a1b1+a2b2+...+anbn)^2<=(a1^2+a2^2+...+an^2)(b1^2+b2^2+...+bn^2)
where ai, bi are real numbers, i=1,2,...,n

Purchase this Solution
Solution Summary

An inequality is proven using unit vectors. Function vectors are examined.

Solution Preview

Proof. Consider two vectors x=(a1,a2,...,an) and y=(b1,b2,...,bn). If all ai's are equal zero or all bi's are equal zero, then x=(0,0,...,0) ...

Solution provided by:
Changping Wang, MA
Education
  • BSc , Wuhan Univ. China
  • MA, Shandong Univ.
Recent Feedback
  • "Your solution, looks excellent. I recognize things from previous chapters. I have seen the standard deviation formula you used to get 5.154. I do understand the Central Limit Theorem needs the sample size (n) to be greater than 30, we have 100. I do understand the sample mean(s) of the population will follow a normal distribution, and that CLT states the sample mean of population is the population (mean), we have 143.74. But when and WHY do we use the standard deviation formula where you got 5.154. WHEN & Why use standard deviation of the sample mean. I don't understand, why don't we simply use the "100" I understand that standard deviation is the square root of variance. I do understand that the variance is the square of the differences of each sample data value minus the mean. But somehow, why not use 100, why use standard deviation of sample mean? Please help explain."
  • "excellent work"
  • "Thank you so much for all of your help!!! I will be posting another assignment. Please let me know (once posted), if the credits I'm offering is enough or you ! Thanks again!"
  • "Thank you"
  • "Thank you very much for your valuable time and assistance!"
Purchase this Solution
Free BrainMass Quizzes
Graphs and Functions

This quiz helps you easily identify a function and test your understanding of ranges, domains , function inverses and transformations.

Exponential Expressions

In this quiz, you will have a chance to practice basic terminology of exponential expressions and how to evaluate them.

Solving quadratic inequalities

This quiz test you on how well you are familiar with solving quadratic inequalities.

Probability Quiz

Some questions on probability

Multiplying Complex Numbers

This is a short quiz to check your understanding of multiplication of complex numbers in rectangular form.

View More Free Quizzes
Related BrainMass Solutions

  • Vectors in linear algebra

    NOTE: This is just the reverse of the Cauchy- Schwatrz inequality for the ordinary dot product. Proof. Let , then we have , , So, So, So, This is a proof of the reverse of the Cauchy-Schwartz dot product inequality.

  • Proof for Vectors

    Using Schwartz, inequality, a vector identity is proved in the solution.

  • Weighted Means

    Alternate Method: Define two vectors and , and Using the property We have the required result A proof involving weighted means is provided. The solution is detailed and well presented.

  • Inner Products for Unit Vectors

    Let be unit vectors in such that . Give a necessary and sufficient relationship between and Statement. Under those hypotheses, we have if and only if Proof. Sufficiency.

  • Find the smallest and largest values possible for ||V - W||.

    Proof of (1): Assume that the angle between V and W is . We use denotes the dot product of V and W. Note that as the angle between V and V is zero. Hence, Use the fact that .

  • Perpendicular Planes, Line Parallel to a Plane and Normal Unit Vectors

    Thanks for using BrainMass. Perpendicular Planes, Line Parallel to a Plane and Normal Unit Vectors are investigated. The solution is detailed and well presented.

  • Inner product spaces

    This is a proof of orthogonality and unit vectors, and shows how to determine distance between vectors.

  • Hilbert Space and Subspace

    Thanks for using BrainMass. Problem. Show that if is an orthonormal set in a Hilbert space H, then the set of all vectors of the form is a subspace of H. Hint: Take a Cauchy sequence , where .

  • Epsilon-delta limits

    You could clearly come up a function for which this was not true: r = x.i + y.j + z.k (where i,j, and k are the unit basis vectors of R^3) f(r) = xyz here, Lim f(r) = 0 r->0 Once you have your function

View More Related Solutions