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題組內容

Problem 5 (15%) Let C be a circle |z|=2 described in the counterclockwise direction.

(a)(5%) Compute the following integral
, n is a positive integer

其他申論題

(b) If Ω1 , that is , is an orthogonal matrix, then what mathematical relation between A and ATcan be derived? (5%)

(c) If Ωa. is an idempotent matrix, then what are all possible values of det A ? (5%)

(a) Write out the set,where N(●)and R(●) indicate the null space and the range of a matrix, respectively. (5%)

(b) Consider the inner product space V =, where ＜A,B) :=tr(ATB) for A and B in . Describe Sh as the span of a set of orthonormal vectors in . (7%)

(b)(10%) Suppose the answer you obtained in Part (a) is jnt . Use Part (a) to evaluate

Problem 6(15%) Define the Fourier transform of a signal dt, and its inverse Fourier ransform is . It is already known that the Fourier transform of signal x(i)=sin(ai) /(πi) is and 9.Compute the Fourier transform of the signal

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沒有【段考】高二英文下學期權限，請先開通．

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