Practice - Best Approximation in Inner Product Spaces
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
Define best approximation in your own words.
💡 Hint: Think about it as finding the nearest point.
What does the error vector signify?
💡 Hint: Look for a relationship between the original and approximated values.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is the best way to define best approximation?
💡 Hint: Refer back to the definition discussed in class.
The error vector is known for being orthogonal to what?
💡 Hint: Remember the definition of the Projection Theorem.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
Given a vector v = (4, 3) and a subspace defined by w1 = (1, 1) and w2 = (1, -1), find the best approximation vector v_b.
💡 Hint: Break down the steps using projection formulas.
In a practical setting, if you have a data set with noise and want to fit your model optimally using least squares, how would you identify the best parameters?
💡 Hint: Utilize derivatives to find minima in your functions.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.