matplotlib colorbar alternating top bottom labels

Question

First of all, this was intended as a self-answer question, because I believe it would be helpful in certain situations, e.g. in this post the author tried to hide

Answer 1

You could add a twin Axes object and set every odd ticks there while setting every even ticks on the original Axes.

import numpy as np
import matplotlib.pyplot as plt

# Make the plot
fig, ax = plt.subplots(1,1, figsize=(5,5))
fig.subplots_adjust(bottom=0.2)
## Trick to have the colorbar of the same size as the plot
box = ax.get_position() 
cax = fig.add_axes([box.xmin, box.ymin - 0.1, box.width, 0.03])
m = ax.matshow(np.random.random(100).reshape(10,10), aspect="auto") # Don't forget auto or the size of the heatmap will change.
cb = plt.colorbar(m, cax=cax, orientation="horizontal")

# Add twin axes 
cax2 = cax.twiny()

# get current positions and values of the ticks.
# OR you can skip this part and set your own ticks instead.
xt = cax.get_xticks()
xtl = [i.get_text() for i in cax.get_xticklabels()]

# set odd ticks on top (twin axe)
cax2.set_xticks(xt[1::2])
cax2.set_xticklabels(xtl[1::2])
# set even ticks on  original axes (note the different object : cb != cax)
cb.set_ticks(xt[::2])
cb.set_ticklabels(xtl[::2])

HTH