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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What does the QR algorithm compute?
💡 Hint: Think about what eigenvalues tell us about transformations.
Question 2
Easy
What are the two components of QR decomposition?
💡 Hint: One is orthogonal, the other has zeros below the diagonal.
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 two matrices does the QR algorithm decompose a matrix into?
- Upper triangular and diagonal
- Orthogonal and lower triangular
- Orthogonal and upper triangular
💡 Hint: Recall the properties of Q and R.
Question 2
True or False: The QR algorithm can only be used for symmetric matrices.
- True
- False
💡 Hint: Consider the general applicability in engineering.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given a symmetric matrix, explain why the QR algorithm would likely converge faster than for a non-symmetric matrix.
💡 Hint: Focus on the properties of symmetry and how they relate to matrix behavior.
Question 2
Illustrate a civil engineering scenario that requires the application of the QR algorithm, detailing the benefits it offers.
💡 Hint: Consider the dynamic response of structures to external forces.
Challenge and get performance evaluation