Practice Orthogonality And Orthonormality (27.4) - Inner Product Spaces
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Orthogonality and Orthonormality

Practice - Orthogonality and Orthonormality

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define orthogonal vectors.

💡 Hint: Think about their angle with respect to each other.

Question 2 Easy

What conditions must a set of vectors meet to be considered orthonormal?

💡 Hint: Recall the properties of orthogonality and length.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What defines two vectors as orthogonal?

Their lengths are equal
Their inner product equals zero
They lie in the same direction

💡 Hint: Think about what it means for two lines to meet.

Question 2

True or False: An orthonormal set can contain vectors that are not of unit length.

True
False

💡 Hint: Consider the criteria for orthonormal sets.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given two vectors u = (2, -1) and v = (-0.5, 1) in R^2, determine if they are orthogonal.

💡 Hint: Find the inner product to check their orthogonality.

Challenge 2 Hard

Assert whether the following set of vectors forms an orthonormal set: A = { (1,0), (0,1), (1,1)/√2, (1,-1)/√2 }.

💡 Hint: Evaluate each vector's length and their pairwise inner products.

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Reference links

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