Update elements of dataframe by applying function involving same row elements

You can use reshape columns i and j and subtract,

df = df.iloc[:, :8].sub(df['i'].values[:, None]).div(df['j'].values[:, None]).round(2)

    a       b       c       d       e       f       g       h
0   8.18    17.27   26.36   35.45   44.55   53.64   62.73   71.82
1   90.00   98.33   106.67  115.00  123.33  131.67  140.00  148.33
2   159.23  166.92  174.62  182.31  190.00  197.69  205.38  213.08
3   218.57  225.71  232.86  240.00  247.14  254.29  261.43  268.57

Make use of filter and the underlying numpy arrays.

u = df.filter(regex='[^ij]')

res = (u.values - df.i.values[:, None]) / df.j.values[:, None]

pd.DataFrame(res, columns=u.columns)

            a           b           c           d           e           f           g           h
0    8.181818   17.272727   26.363636   35.454545   44.545455   53.636364   62.727273   71.818182
1   90.000000   98.333333  106.666667  115.000000  123.333333  131.666667  140.000000  148.333333
2  159.230769  166.923077  174.615385  182.307692  190.000000  197.692308  205.384615  213.076923
3  218.571429  225.714286  232.857143  240.000000  247.142857  254.285714  261.428571  268.571429

Try using sub and div with index slicing:

df.loc[:, 'a':'h'] = df.loc[:, 'a':'h'].sub(df['i'], axis=0).div(df['j'], axis=0)

Output:

            a           b           c           d           e           f  \
0    8.181818   17.272727   26.363636   35.454545   44.545455   53.636364   
1   90.000000   98.333333  106.666667  115.000000  123.333333  131.666667   
2  159.230769  166.923077  174.615385  182.307692  190.000000  197.692308   
3  218.571429  225.714286  232.857143  240.000000  247.142857  254.285714   

            g           h    i     j  
0   62.727273   71.818182  0.1  0.11  
1  140.000000  148.333333  0.2  0.12  
2  205.384615  213.076923  0.3  0.13  
3  261.428571  268.571429  0.4  0.14