” 写作program课程程序、 辅导Matlab实验程序、Matlab编程HW 2 Matlab (10pts)Download the code ConditionandErrorsm.m. Explain the results of the code mathematically.What is being calculated? What do the results show? Use different choices for the error toassist with your Explanation. It is not sufficient to run the code and give the results withoutexplanation. Your score will be 1 pt if you have just demonstrated that you can downloadthe code and run. For the full 10 pts you must explain mathematically what is going on.Explain (mathematics not the coding) for the attached code. Experiment with differentchoices of the error. (10 points)HW 2 Theoretical Questions: Norms and Eigenvalues (20pts)1. Let A of size m m be complex and Hermitian. An eigenvector of A is a nonzerovector x Cm such that Ax = x for some C, the corresponding eigenvalue.(a) Prove that all Eigenvalues of A are real(b) Prove that if x and y are distinct eigenvectors corresponding to distinct eigenvalues,then x and y are Orthogonal.2. Let S be complex of size m m be skew Hermitian S = S.(a) Prove that the eigenvalues of S are pure imaginary. (ie the eigenvalues are all ofthe form = x for some x and Real() = 0(b) Prove that I S is nonsingular.(c) Prove that the matrix Q = (I S)1(I + S) is unitary. This is the Cayleytransform of S. 写作program课程作业、 辅导Matlab实验作业3. It u and v are vectors of length m, the matrix A = I + uvis known as a rank oneperturbation of the identity.(a) Prove that if A is nonsingular, then its inverse has the form A1 = I + uvforsome Scalar . (i.e. verify that this is the inverse).(b) What is ? Show how you found .(c) For what u and v is A singular? Prove your statement.(d) If it is singular, what is null(A)? Why? Explain.1Basic Background on Norms.Prove each of these statements1. For the inner product defined by x, y =Xixiyi(a) x, y = y, x .(b) x, y + z = x, y + x, z (c) The Cauchy Schwartz inequality| x, y | x, x y, y .2. The inequalities which relate the 1, 2 and norms.(a) ||x||2 ||x||1 n||x||2 You will Need to use Holders inequality for complexnumbers ai, where max denotes the largest eigenvalue of the givenmatrix.4. The inequalities Which relate the 1, 2 and matrix norms for square matrices ofdimension n.如有需要，请加QQ：99515681 或邮箱：99515681@qq.com
“
添加老师微信回复‘’官网 辅导‘’获取专业老师帮助，或点击联系老师1对1在线指导。
