"The title of this book deserves an explanation. Most linear algebra textbooks use determinants to prove that every linear operator on a finite-dimensional complex vector space has an eigenvalue. 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 operator is not invertible if and only if its determinant equals 0, and then define the characteristic polynomial. This tortuous (torturous?) path gives students little feeling for why eigenvalues exist.
In contrast, the simple determinant-free proofs presented here (for example,
see 5.19) offer more insight. Once determinants have been moved to the end of the book, a new route opens to the main goal of linear algebra—understanding the structure of linear operators."
“Be careful not to confuse tortuous with torturous. These two words are relatives—both ultimately come from the Latin verb torquere, which means "to twist," "to wind," or "to wrench"—but tortuous means "winding" or "crooked," whereas torturous means "painfully unpleasant."
There is a meeting or mismeeting between book and reader in math. Sometimes you are on the wrong footing to absorb a book. You bounce. Maybe you come back later and absorb the book.
As far as the title, just catching marketing I think. Might not appeal to all for sure.
"The title of this book deserves an explanation. Most linear algebra textbooks use determinants to prove that every linear operator on a finite-dimensional complex vector space has an eigenvalue. 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 operator is not invertible if and only if its determinant equals 0, and then define the characteristic polynomial. This tortuous (torturous?) path gives students little feeling for why eigenvalues exist.
In contrast, the simple determinant-free proofs presented here (for example, see 5.19) offer more insight. Once determinants have been moved to the end of the book, a new route opens to the main goal of linear algebra—understanding the structure of linear operators."