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numpy: Exercises
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#. Implement a function that takes a ``d`` dimensional vector ``x``
   returns their Euclidean norm.

   .. hint::
       The Euclidean norm of a vector is the square root of its dot product
       with itself.

#. Implement a function that takes two ``d`` dimensional vectors ``x`` and ``z``
   and returns their Euclidean distance.

   .. hint::
       Can you re-use the solution of the previous exercise?

#. Implement a function that takes a matrix ``A`` and an integer ``k``, and
   returns ``A`` elevated to the ``k`` th power.

#. Write a Python program that plots the data here::

    https://drive.google.com/open?id=0B0wILN942aEVVlk4TS1WaDItVU0

   Every row has an experiment ID and a value; there are 10 experiments, and
   100 values (rows) per experiment. For each experiment, plot its values as a
   time series.

   The plot the average time series, i.e. the average curve, where the average
   is taken over all experiments.

   .. hint::
       Use ``matplotlib.pyplot`` and the ``plot(x, y)`` function, as done in
       the examples above, to plot the ten curves and their mean.

#. Implement the Power Iteration method for finding the largest eigenvalue and
   eigenvector of a matrix, as described in the first paragraph of:

    https://en.wikipedia.org/wiki/Power_iteration#The_method

   Check that it matches the results given by the ``eig()`` method of the
   ``linalg`` module.

#. Implement the Gram-Schmidt orthogonalization routine, described here:

       https://en.wikipedia.org/wiki/Gram%E2%80%93Schmidt_process

#. Given the *iris dataset*, compute the covariance matrix of the petal
   lenght and petal widht for the *iris setosa* rows.

   .. hint::
       The covariance matrix is defined here:

           https://en.wikipedia.org/wiki/Covariance_matrix