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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define orthogonality in the context of functions.
π‘ Hint: Think about the relationship between their inner product and overlap.
Question 2
Easy
What is an inner product for continuous functions?
π‘ Hint: Remember the formula for the inner product!
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 does it mean for two functions to be orthogonal?
- They overlap entirely
- Their inner product is zero
- They can be represented as linear combinations
π‘ Hint: Think about the inner product definition!
Question 2
True or False: sin(t) and cos(t) are orthogonal functions.
- True
- False
π‘ Hint: Review the definition of the inner product.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Prove that the functions sin(kt), cos(kt) for different k are orthogonal over the interval [0, 2Ο].
π‘ Hint: Utilize properties of integral and orthogonality.
Question 2
Show that any square-integrable function can be expressed using a complete orthogonal set.
π‘ Hint: Consider the Fourier series representation.
Challenge and get performance evaluation