MATH307 December 2008
• Q1 • Q2 • Q3 • Q4 • Q5 • Q6 (a) • Q6 (b) • Q7 • Q8 • Q9 • Q10 •
Consider the symmetric matrix
Compute the matrix norms and
Make sure you understand the problem fully: What is the question asking you to do? Are there specific conditions or constraints that you should take note of? How will you know if your answer is correct from your work only? Can you rephrase the question in your own words in a way that makes sense to you?
If you are stuck, check the hint below. Consider it for a while. Does it give you a new idea on how to approach the problem? If so, try it!
The infinity norm of a matrix is simply the maximum absolute row sum of the matrix, that is, the largest 1-norm of its rows.
The 2-norm for a symmetric matrix is the largest absolute value of the eigenvalues.
Checking a solution serves two purposes: helping you if, after having used the hint, you still are stuck on the problem; or if you have solved the problem and would like to check your work.
- If you are stuck on a problem: Read the solution slowly and as soon as you feel you could finish the problem on your own, hide it and work on the problem. Come back later to the solution if you are stuck or if you want to check your work.
- If you want to check your work: Don't only focus on the answer, problems are mostly marked for the work you do, make sure you understand all the steps that were required to complete the problem and see if you made mistakes or forgot some aspects. Your goal is to check that your mental process was correct, not only the result.
Found a typo? Is this solution unclear? Let us know here.
Please rate my easiness! It's quick and helps everyone guide their studies.
The infinity norm of a matrix is the infinity norm of the vector whose entries are the 1-norm of each row, so it will be
The 2-norm of a matrix is the largest of the absolute values of the eigenvalues. So we need to calculate the eigenvalues of A as the roots of the characteristic polynomial
Hence, the eigenvalues of A are and . The 2-norm of A is the largest of the absolute values of these and therefore = .
Click here for similar questions
MER QGH flag, MER QGQ flag, MER QGS flag, MER RT flag, MER Tag Matrix norm, Pages using DynamicPageList parser function, Pages using DynamicPageList parser tag