Normalize columns of pandas data frame

one easy way by using Pandas: (here I want to use mean normalization)

normalized_df=(df-df.mean())/df.std()

to use min-max normalization:

normalized_df=(df-df.min())/(df.max()-df.min())

Edit: To address some concerns, need to say that Pandas automatically applies colomn-wise function in the code above.

You can use the package sklearn and its associated preprocessing utilities to normalize the data.

import pandas as pd
from sklearn import preprocessing

x = df.values #returns a numpy array
min_max_scaler = preprocessing.MinMaxScaler()
x_scaled = min_max_scaler.fit_transform(x)
df = pd.DataFrame(x_scaled)

For more information look at the scikit-learn documentation on preprocessing data: scaling features to a range.

Based on this post: https://stats.stackexchange.com/questions/70801/how-to-normalize-data-to-0-1-range

You can do the following:

def normalize(df):
    result = df.copy()
    for feature_name in df.columns:
        max_value = df[feature_name].max()
        min_value = df[feature_name].min()
        result[feature_name] = (df[feature_name] - min_value) / (max_value - min_value)
    return result

You don't need to stay worrying about whether your values are negative or positive. And the values should be nicely spread out between 0 and 1.