Short colorbar

.py

import matplotlib.pyplot as plt
import mpl_toolkits.axes_grid1.inset_locator

fig, ax = plt.subplots()

matrix = np.random.normal(size=(100, 100))
sm = ax.matshow(matrix)

# Attach a small axes to the lower right of the main axes. It's an "inset"
# placed outside of the plot. The size is 0.02 width x 0.5 height of the
# main axes.
cbar_ax = mpl_toolkits.axes_grid1.inset_locator.inset_axes(
    ax,
    width="100%", height="100%",
    bbox_to_anchor=(1.02, 0, 0.02, 0.5), bbox_transform=ax.transAxes,
    borderpad=0
)
cbar = fig.colorbar(sm, cax=cbar_ax)

# If you favor an unbordered colorbar.
cbar.outline.set_edgecolor("none")