Lecture Slides 9

Lecture Slides 9 - AMS 210: Applied Linear Algebra October...

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AMS 210: Applied Linear Algebra October 8, 2009 AMS 210
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Topics Today Problem Set 3 Grades Problem Set 5 Matrix Norms Properties Use of Matrix Norm in Error Bounds Stable Probability Vector for Weather Markov Chain Eigenvectors and Growth Models Matrix Partitioning AMS 210
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Problem Set 3 Grades and solution on Blackboard. Maximum possible (and achieved) grade of 100. Average of 80, standard deviation of 15, and a median grade of 85. Standard deviation and median almost identical to problem set 2. Average 3 points lower. AMS 210
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Problem Set 5 This week’s problem set is due next Thursday, October 15. Read sections 2.5 and 2.6. Exercises: 2.5: 26ab, 27a, 28; 2.6: 1ad, 3a, 6c, 7, 9. Show work. AMS 210
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Matrix Norm Properties | r || x | = | r x | and || r A || = | r | · || A || || AB || ≤ || A || · || B || || A k || ≤ ( || A || ) k || A + B || ≤ || A || + || B || AMS 210
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Use of Matrix Norm in Error Bounds Already seen that matrix norms specify bounds on behavior of matrices as operating on vectors. Can use this to determine bounds on sensitivity of systems on
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Lecture Slides 9 - AMS 210: Applied Linear Algebra October...

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