27.3 - Norm Induced by Inner Product
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
What is the formula for the norm of a vector in an inner product space?
💡 Hint: Recall how the inner product is used to determine the norm.
Is the norm ever negative? Why or why not?
💡 Hint: Think about the properties of lengths or distances.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the norm of a vector defined as?
💡 Hint: Think about how we calculate the distance or length.
True or False: The norm of a vector can be negative.
💡 Hint: What do you know about lengths?
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
Given vector a = (3, 4) and b = (1, 2), calculate the distance between these two vectors using their norms.
💡 Hint: Remember that distance can be found using the norm of the difference between the vectors.
Prove that the norms behave correctly under scalar multiplication by showing how ∥2v∥ relates to ∥v∥.
💡 Hint: Use the definition of the norm with the inner product to show this relationship.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.