EE103 Spring 2010, HW 5 Solution Set, Prof S.E. Jacobsen Page 1 / 5 Applied Numerical Computing Instructor: Prof. S. E. Jacobsen HW5 Solution Set Problem 1. (a)Since Pis orthogonal, we have TP PI, and we have PALU. Then, we have TTTAU L P(1) Then TA ydcan be expressed as TTU L Pyd(2) Or, we may rewrite (2) as ()TTU LPydWe then have ,,TTTTzLPyU zdprovides zuPyL uzprovides uyP u(b)()y rowsu. Students, you should generate a small example to see that this result is correct. Problem 2. (a)Since N is orthonormal, NTN = I. Then 2222() ()TTTTTNxNxNxx N Nxx Ixx xx, (b)One may observe the L.H.S. of the equation, stated in the question, is 12121122,,...,,,...,(...)TkkTTkkTIqqqqqqIq qq qq q Since the orthogonality between qiand qj, 1 ≤i, j≤k, gives qiTqj= 0, the R.H.S., of the equation, stated in the question, is
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