Form expression

Find a closed form expression for µ and prove that your answer is correct.

  1. (10 points) Not all norms behave the same; for instance, the 1-norm of a vector can be dramatically different from the2-norm, especially in high dimensions. Prove the following
    norm inequalities for d-dimensional vectors, starting from the definitions provided in class and
    lecture notes. (Use any algebraic technique/result you like, as long as you cite it.)
    a. kxk∞ ≤ kxk2 ≤

    dkxk∞
    b. kxk∞ ≤ kxk1 ≤ dkxk∞
  2. (10 points) In this problem, you will practice using Python for exploratory data analysis.
    • Open the Colab notebook from the following URL: click here
    • Use File > Save a Copy in Drive to create an editable copy in your own Google Drive
    • As you work through the notebook, look for the text and code cells marked with a TODO
    at the top. In these cells, answer the questions or fill in code as indicated.
    • When you are finished, run the entire notebook from beginning to end, using Runtime >
    Run All. Check the output and make sure everything looks OK.
    • Then, you can save your notebook as a PDF (to upload along with the rest of your
    submission) using File > Print.

This question has been answered.

Get Answer