Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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 related to the topic.
Question 1
Easy
What defines a Hilbert space?
💡 Hint: It relates to convergence of sequences.
Question 2
Easy
Give an example of a Hilbert space.
💡 Hint: Think of sequences whose squares sum up to a finite value.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is a Hilbert space?
- A type of matrix
- A complete inner product space
- A specific numerical method
💡 Hint: It involves sequences in the discussion.
Question 2
True or False: In a Hilbert space, not every Cauchy sequence converges.
- True
- False
💡 Hint: Consider the definition of completeness.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that a given sequence defined as a_n = 1/n^2 is a Cauchy sequence in ℓ2.
💡 Hint: Focus on the square sums and their convergence as n approaches infinity.
Question 2
How does the concept of orthogonality in L2[a,b] relate to Fourier series?
💡 Hint: Consider how functions interact when integrated over an interval.
Challenge and get performance evaluation