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# Equivalence theorem for nonsingular matrices: the matrix A does not have 0 as an eigenvalue.

Put content here**Theorem:** An $n \times n$ matrix $A$ is nonsingular iff 0 is not an eigenvalue of $A$. If 0 were an eigenvalue, there would exist a nonzero $v$ with $Av = 0v = 0$, making $A$ singular.

# Parents

* Nonsingular matrices and equivalences