I have a linear relation between a dependent and an independent variable (x and y). I need to prove that x and y are equivalent. To do that I have already considered two ways: 1-verifying reflexivity, symmetry and transitivity; and 2- proving that it is a bijective function. If this is right, I have already done the first step. As a second task I have to extend this relation to fuzzy sets and I only need to prove min-max transitivity at present.
I need to build the adjacency matrix of such relation to demonstrate the rest of the properties and I think I should get a identity matrix representing variables x and y, but I don´t know if there is any theorem about this. That´s to say: If the linear ecuation is bijective, the adjacency matrix of such relationship is necessary an identity matrix?
Please I dont understand your question
What is the link between linear functions and matrices
Dear Mohammed, thank´s for replying!. Sorry if I did not explained properly.
I have a linear relation between a dependent and an independent variable (x and y). I need to prove that x and y are equivalent. To do that I have already considered two ways: 1-verifying reflexivity, symmetry and transitivity; and 2- proving that it is a bijective function. If this is right, I have already done the first step. As a second task I have to extend this relation to fuzzy sets and I only need to prove min-max transitivity at present.
I need to build the adjacency matrix of such relation to demonstrate the rest of the properties and I think I should get a identity matrix representing variables x and y, but I don´t know if there is any theorem about this. That´s to say: If the linear ecuation is bijective, the adjacency matrix of such relationship is necessary an identity matrix?
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