Science:Math Exam Resources/Courses/MATH307/December 2008/Question 07/Solution 1
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 .