24.17 - Orthogonality in Vector Spaces
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
Define orthogonal vectors.
💡 Hint: Think about their geometric representation.
What condition must be met for vectors to be orthonormal?
💡 Hint: Recall the definition of unit length.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does it mean for two vectors to be orthogonal?
💡 Hint: Think about how two vectors' directions relate in space.
True or False: All orthonormal vectors are orthogonal.
💡 Hint: Recall the definition of orthonormal sets.
1 more question available
Challenge Problems
Push your limits with advanced challenges
Given vectors A = (2, 3, 6) and B = (1, -1, 2), are they orthogonal? Verify your answer.
💡 Hint: Remember to calculate the dot product correctly.
Find a new orthonormal basis for the vectors in R² given by (4, 3) and (1, 1) using the Gram-Schmidt process.
💡 Hint: Follow the Gram-Schmidt steps methodically.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.