Due on Feb 20

  1. For a square matrix \(A\), prove that \((A^{-1})^\top = (A^\top)^{-1}\). (5 points)

  2. Find the gradient of \(f(A)=X^\top A X\) with respect to \(A\), where \(X\) is a column vector and \(A\) is a matrix. Note that \(A\) is the variable here, rather than \(X\) as discussed in class. (5 points)

  3. Try to build a linear regression model to predict the stock price of MSFT from the prices of several other stocks. You can download the Jupyter notebook of the question from here. (10 points)