A Schmidt decomposition - How do I find the matrix related to the state?

Arquimedes
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How to writte the matrix associated to the state, so I can apply the Singular Value Decomposition to that matrix and get the Schmidt coefficients.
Hello, I am currently studying the Schmidt decomposition and how to use it to determine if a state is entangled or not and I can't understand how to write the state as a matrix so I can apply the Singular Value Decomposition and find the Schmidt coefficients. The exercise I am trying to complete is this one:;

problem25.png
 
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A general mapping from ##\mathbb{C}^2\otimes\mathbb{C}^3## to ##\mathbb{C}^6## may be written,

##v_i = \sum_{k=1}^2 \sum_{m=1}^3 \alpha_{i k m} u_k w_m##

there are 36 unspecified constants, ##\alpha_{i k m}##. So there are many possibilities. I think the problem statement is incomplete?
 
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