Science:Math Exam Resources/Courses/MATH307/December 2008/Question 07
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Question 07 

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! 
Hint 

The infinity norm of a matrix is simply the maximum absolute row sum of the matrix, that is, the largest 1norm of its rows. The 2norm for a symmetric matrix is the largest absolute value of the eigenvalues. 
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Solution 

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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 1norm of each row, so it will be
Hence, the eigenvalues of A are and . The 2norm of A is the largest of the absolute values of these and therefore . 