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Geršgorin And Beyond•••, Jason Knight Belnap

Undergraduate Honors Capstone Projects

Eigenvalues are useful in various areas of mathematics, such as in testing the critical values of a multi variable function to see if it is a local extrema. One of the more common ways to define eigenvalues is:

Definition (1): Given that A is an n by n matrix, λ is an eigenvalue of A if and only if det(A - λI_n) = 0. Any nonzero vector in Null(A - λI) is called an eigenvector associated with λ.