# Today I Learned

Some of the things I've learned every day since Oct 10, 2016

## 5: Eigenvalues and Invertibility

If $A$ is an $n \times n$ matrix and $\lambda_1, \lambda_2, \lambda_3 \dots \lambda_n$ are its $n$ (not necessarily distinct) eigenvalues, then the determinant of $A$ is the product of those eigenvalues. From this, it follows that $A$ is invertible if and only if each of those eigenvalues is nonzero, since a matrix is invertible if and only if its determinant is nonzero.