Mathematical Experiment 9

  1. Design an experiment to find the minimum value of ||A-X|| , where A is a given n-by-m matrix as X runs through rank 1 m-by-n matrices. Here the norm of a matrix ||M|| could be any one of the following:
    1. a. ||M|| = åi,j|mi,j|
    2. b. ||M|| = max|mi,j|
    3. c. ||M|| = (åi,j|mi,j|2)1/2.

    4. Try the case that the entries taken from real scalars and the case the entries are taken from integers.
  2. Given finitely many points on the plane, the least connect set containing all these points takes the form of a tree with the points as some of the nodes. Perform an experiment to find out the shape of the tree of minimum length.
  3. Draw a regular icosahedron. Rotate it.
  4. Draw a regular dodecahedron. Rotate it.
  5. Draw the above figures with the plotter.