is there a way to normalize [-3,1] to ${\begin{bmatrix} \dfrac{-3}{\sqrt{10}}\\ \dfrac{1}{\sqrt{10}}\\ \end{bmatrix}}$ with python?
You have already computed that, but you've not bound the output to a variable, also called name in python. Try the following snippet:

result = np.linalg.norm(v1,ord=2,axis=1,keepdims=True)
print(result)



Based on the edit, I update the answer. As you may find answers to your question, a typical way to find what you need is something like the following function:

def normalize(v):
    norm = np.linalg.norm(v)
    if norm == 0: 
       return v
    return v / norm


Equivalently, there is a function called normalize in sklearn.preprocessing which can be employed for your task.