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Determinant Theorem


Given a square matrix M, the following are equivalent:

1. |M|!=0.

2. The columns of M are linearly independent.

3. The rows of M are linearly independent.

4. Range(M) = R^n.

5. Null(M) = {0}.

6. M has a matrix inverse.


See also

Determinant, Matrix Inverse, Null Space, Range

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Cite this as:

Weisstein, Eric W. "Determinant Theorem." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/DeterminantTheorem.html

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