display matrix values and colormap

In Jupyter notebooks this is also possible with DataFrames and Seaborn:

import numpy as np
import seaborn as sns
import pandas as pd

min_val, max_val = 0, 15
intersection_matrix = np.random.randint(0, 10, size=(max_val, max_val))
cm = sns.light_palette("blue", as_cmap=True)
x=pd.DataFrame(intersection_matrix)
x=x.style.background_gradient(cmap=cm)
display(x)

You need to use ax.matshow not plt.matshow to make sure they both appear on the same axes.

If you do that, you also don't need to set the axes limits or ticks.

import numpy as np
import matplotlib.pyplot as plt

fig, ax = plt.subplots()

min_val, max_val = 0, 15

intersection_matrix = np.random.randint(0, 10, size=(max_val, max_val))

ax.matshow(intersection_matrix, cmap=plt.cm.Blues)

for i in xrange(15):
    for j in xrange(15):
        c = intersection_matrix[j,i]
        ax.text(i, j, str(c), va='center', ha='center')

Here I have created some random data as I don't have your matrix. Note that I had to change the ordering of the index for the text label to [j,i] rather than [i][j] to align the labels correctly.