Practice Qr Algorithm For Eigenvalue Computation (29.11)

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6 sample questions

Question 1.
What does the QR algorithm compute?
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Think about what eigenvalues tell us about transformations.
Question 2.
What are the two components of QR decomposition?
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One is orthogonal, the other has zeros below the diagonal.
3Question 3.
What two matrices does the QR algorithm decompose a matrix into?
- Upper triangular and diagonal
- Orthogonal and lower triangular
- Orthogonal and upper triangular
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Recall the properties of Q and R.
4Question 4.
True or False: The QR algorithm can only be used for symmetric matrices.
- True
- False
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Consider the general applicability in engineering.
Question 5.
Given a symmetric matrix, explain why the QR algorithm would likely converge faster than for a non-symmetric matrix.
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Focus on the properties of symmetry and how they relate to matrix behavior.
Question 6.
Illustrate a civil engineering scenario that requires the application of the QR algorithm, detailing the benefits it offers.
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Consider the dynamic response of structures to external forces.

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