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Equivalence theorem for nonsingular matrices: the linear transformation given by T(x)=Ax has an inverse.

Created over 8 years ago, updated 10 days ago

Theorem: An $n \times n$ matrix $A$ is nonsingular iff $T(x) = Ax$ has an inverse transformation $T^{-1}$. The inverse transformation is given by $T^{-1}(y) = A^{-1}y$.