Question: Adding dependencies to a defined variable

Can we define dependencies of a variable after using the variable? For example, let us take,

f:=2*T+x^2;

Here, T has no dependencies. What should we do to make it dependent of x and y without redefining the whole thing as f:=2*T(x,y)+x^2;

and, can we do this for a whole matrix or vector?

 

 

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