Explore BrainMass

# Linear Algebra : Norms

Not what you're looking for? Search our solutions OR ask your own Custom question.

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

For any x=(x1,....,xn), let us try to define a norm two ways. Consider

(a) ||X||1=summation |Xi| from i=1 to n

(b) ||X||b=summation |xi-xj| from i,j=1 to n

Does either one of these formulas define a norm? If yes, show that all three axioms of norm hold. If no, demonstrate which axiom fails.

Â© BrainMass Inc. brainmass.com June 7, 2023, 2:27 pm ad1c9bdddf
https://brainmass.com/math/linear-algebra/linear-algebra-norms-11651

#### Solution Preview

Please see the attached file for the full solution.

Thanks ...

#### Solution Summary

Summations are investigated as to whether they define norms. The solution is detailed and well presented. The formulas to define a norm are given.

\$2.49

### Free BrainMass Quizzes

• Exponential Expressions

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

• Graphs and Functions

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

• Probability Quiz

Some questions on probability

• Geometry - Real Life Application Problems

Understanding of how geometry applies to in real-world contexts

• Know Your Linear Equations

Each question is a choice-summary multiple choice question that will present you with a linear equation and then make 4 statements about that equation. You must determine which of the 4 statements are true (if any) in regards to the equation.

View More Free Quizzes