# numpy: ExercisesΒΆ

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:

Check that it matches the results given by the

`eig()`

method of the`linalg`

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

Given the

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