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# hw1 - Stat 511 Homework 1 corrected Spring 2011 Due 11am...

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Stat 511 Homework 1 - corrected Spring 2011 Due: 11am, Wednesday Jan 19 (because no class Monday Jan 17) Please review Ken Koehlers notes on vectors and matrices, available at http://www.public.iastate.edu/ kkoehler/stat511/sect2.4page.pdf You may skip/skim (for now) the material on eigen and spectral decompositions (pp 78-108). Note that: Dr. Koehler uses A T to indicate matrix transpose. We will use A 0 . His notes have S-PLUS code. My R code, in matrix.r on the class web site, is very similar. frac 13 on p. 115 should be 1 3 . I have indicated a few problems that I expect you to use a computer for. You should be able to do the rest by hand, but I encourage you to check your work with a computer. Let A = 1 2 3 0 1 0 , B = - 1 5 2 - 1 , and C = 0 1 - 1 1 2 1 . 1. Calculate C 0 + A 2. Calculate BA 3. Calculate AB 4. Calculate tr ( B ) 5. The property shown by result 1.10(iii) in Dr. Koehler’s notes is sometimes called the cyclical property of the trace. It can be extended to products of 3 (or more) matrices. For 3 matrices, it is tr ( ABC ) = tr ( CAB ) = tr

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hw1 - Stat 511 Homework 1 corrected Spring 2011 Due 11am...

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