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 is the formula for the inner product in complex vector spaces?
💡 Hint: Consider the definition that includes complex conjugates.
Question 2
Easy
What does the complex conjugate of (3 + 4i) equal?
💡 Hint: Remember, it changes the sign of the imaginary part.
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 the inner product of the vectors u = (1+i, 2-i) and v = (i, 3+2i)?
💡 Hint: Make sure to apply the complex conjugate appropriately.
Question 2
True or False: The inner product in complex vector spaces always results in a real number.
- True
- False
💡 Hint: Consider the properties of positive definiteness.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given u = (2i, 3-2i) and v = (1+i, 4), calculate the inner product and explain the significance in an application.
💡 Hint: Don't forget to apply the complex conjugate!
Question 2
Discuss how the inner product in complex vector spaces aids in modeling electromagnetic fields. Provide a specific instance.
💡 Hint: Consider how these concepts translate to real-world technology.
Challenge and get performance evaluation