Practice - Definition of Orthogonality (Inner Product Perspective)
Practice Questions
Test your understanding with targeted questions
Define orthogonality in your own words.
💡 Hint: Think about what it means for two lines to meet at a right angle.
What is the inner product of two functions?
💡 Hint: Recall the integral definition discussed in class.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What defines two functions as orthogonal?
💡 Hint: Think about perpendicularity in geometric terms.
True or False: The inner product always results in a complex number.
💡 Hint: What happens to the imaginary part in conjugation?
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Challenge Problems
Push your limits with advanced challenges
Given two functions f1(t) = e^(jt) and f2(t) = e^(-jt), find their inner product over the interval [0, 2π].
💡 Hint: Remember to utilize the integral definition and the property of complex exponentiation.
Prove that any two distinct sines and cosines of the same frequency are orthogonal over any interval of their period.
💡 Hint: Utilize integral properties and sine/cosine identities.
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Reference links
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