How to change legend bar in Matplotlib?

When plotting matrix with imshow in Matplotlib, how to change colorbar legend bar size, location, font and other parameters?

Here I created an example code

import numpy as np
import matplotlib
import matplotlib.pyplot as plt
%matplotlib inline

def plot_matrix(mat, title='example', cmap=plt.cm.Blues):
    plt.imshow(mat, interpolation='nearest', cmap=cmap)
    plt.grid(False)
    plt.title(title)
    plt.colorbar()

data = np.random.random((20, 20))

plt.figure(figsize=(8,8))
plt.tick_params(axis='both', which='major', labelsize=12)

plot_matrix(data) 

In a real use case, I got complex labels and the legend bar becomes much higher then the matrix itself. I want to change the legend bar to make the plot more efficiently use the space.

I found a documentation for the matplotlib.pyplot.colorbar, however have not figure out a good way to set the size, location and font size for the color legend bar.

via Chebli Mohamed