In []: dframe1
Out[]:
letter  A  B  C  D
city
LA      0  1  2  3
SF      4  5  6  7

# Use stack to pivot the columns into the rows
In []: dframe1.stack()
Out[]:
city  letter
LA    A         0
      B         1
      C         2
      D         3
SF    A         4
      B         5
      C         6
      D         7
dtype: int64

# Use unstack to pivot the rows into the columns
# We can choose which level (name) to unstack by
In []: dframe1.stack().unstack()
Out[]:
letter  A  B  C  D
city
LA      0  1  2  3
SF      4  5  6  7