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.

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