Science:Math Exam Resources/Courses/MATH307/April 2009/Question 01 (b)

MATH307 April 2009

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Question 01 (b)
Define the matrix norm for a matrix A.

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

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Solution

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 matrix norm of a matrix A compares $\left|\left|A{\vec {x}}\right|\right|$ to $\left|\left|{\vec {x}}\right|\right|$ where ${\vec {x}}$ is some vector. This comparison between the two terms depends on what ${\vec {x}}$ is, and we want ${\vec {x}}$ that makes $\left|\left|A{\vec {x}}\right|\right|$ the biggest. The matrix norm of A: $\left|\left|A{\vec {x}}\right|\right|={\underset {{\vec {x}};{\vec {x}}\neq 0}{max}}{\frac {\left|\left|A{\vec {x}}\right|\right|}{\|{\vec {x}}\|}}$