Department of Mathematics

Math 583: Mathematical Hacking

ICE 2

Write a Python function that takes three input arguments \(h\), \(k\), and \(n\), and returns the \(n\times n\) matrix below. The \(2\times2\) rotation block has its upper left corner at \(A(k,k)\), where \(0\lt k\lt n\). \[ A = \begin{bmatrix} \frac1h & 0 & \cdots & 0 & 0 & 0 & 0 & \cdots & 0 & -1\\ 0 &\frac1h & \cdots & 0 & 0 & 0 & 0 & \cdots & 0 & -1\\ \vdots & & \ddots & & && & & \vdots & \vdots\\ 0 & 0 & \cdots & \frac1h & 0 & 0 & 0 & \cdots & 0 & -1\\ 0 &0 & \cdots & 0 & \cos\frac{k\pi}n & \sin\frac{k\pi}n & 0 & \cdots & 0 & -1\\ 0 &0 & \cdots & 0 &-\sin\frac{k\pi}n & \cos\frac{k\pi}n & 0 & \cdots & 0 & -1\\ 0 & 0 & \cdots & 0 & 0 & 0 & \frac1h & \cdots & 0 & -1\\ \vdots & \vdots && & && & \ddots & \vdots & \vdots\\ 0 & 0 & \cdots & 0 & 0 & 0 & 0 & \cdots & \frac1h & -1\\ 0 & 0 & \cdots & 0 & 0 & 0 & 0 & \cdots & 0 & \frac1h \\ \end{bmatrix} \]

Mail the completed .py file to the instructor .





Assignment 3 is posted.

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