15.5 Exercises

Ex. 1: Two matrices  are called similar if there exists a matrix , such that . The matrices  and  have the same eigenvalues. Write a test checking that two matrices are similar, by comparing their eigenvalues. Is it a functional or a unit test?

Ex. 2: Create two vectors of large dimensions. Compare the execution time of various ways to compute their dot product:

• SciPy function: v @ w
  
• Generator and sum: sum((x*y for x,y in zip(v,w)))
• Comprehensive list and sum: sum([x*y for x,y in zip(v,w)])

Ex. 3: Let be a vector. The vector  with components

 is called a moving average of . Determine which of the two alternatives to compute  is faster:

v = (u[:-2] + u[1:-1] + u[2:]) / 3

or

v = array([(u[i] + u[i + 1] + u[i + 2]) / 3
  for i in range(len(u)-3)])