26.13 - Orthogonality and Orthonormal Sets
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Practice Questions
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Define orthogonality in your own words.
💡 Hint: Think about the angle between the vectors.
What do we call a set of vectors that are all orthogonal and have unit length?
💡 Hint: Starts with 'o'.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What does it mean for two vectors to be orthogonal?
💡 Hint: Think about the angles between them.
True or False: An orthonormal set can consist of vectors that are not unit vectors.
💡 Hint: Recall the definition of orthonormality.
1 more question available
Challenge Problems
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Given the vectors u = (1, 2) and v = (3, 4), determine if they are orthogonal and convert them into an orthonormal set.
💡 Hint: Check the inner product first before proceeding to the Gram-Schmidt process.
Explain how deriving an orthonormal set can lead to simplifications in a finite element model for structural analysis.
💡 Hint: Think about how calculations are interconnected and reliant on the system of vectors.
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