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

Created almost 9 years ago, updated 6 months 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 $T^{-1}(y) = A^{-1}y$.

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