Hi Julia!
In 2006a MATLAB introduced the colorbar command that automatically adds a colorbar and it can be included underneath any plot function and it will automatically generate a colorbar. For more options type
doc colorbar
into the matlab command window.
As for the second half of your question, you can control the axis direction using
set(gca,'YDir','reverse');
which ought to solve your issue. As for eliminating the values above the diagonal you would have to mess with the data that you are using to generate the heatmap. Since this is in a table (for use with the heatmap command).
Suppose your table is called T, then you may be able to use the following:
for i = 1:size(T,1)-1
T{i,i+1:end} = [];
end
Though I admit my knowledge of tables is severely limited.
