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Anxiety can be as stifling as a broken leg. However, all things being equal, a …

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Sheldon Axler - Determinants
Determinants are difficult, nonintuitive, and often defined without motivation. To prove the theorem about existence of eigenvalues on complex vector spaces, most books must define determinants, prove that a linear map is not invertible if and only if its determinant equals 0, and then define the characteristic polynomial. This tortuous path gives students little feeling for why eigenvalues must exist.