3
$\begingroup$

I keep encountering ostensibly very different branches of mathematics, only to have eigenvalues show up in each one. Is there a single book out there that presents a deep, unified account of the eigenvalue across different fields of math?

1 Answers 1

2

There is exsit a book "Wilkinson - The Algebraic Eigenvalue Problem" I didn't read it.

Actually this is central part of all linear algebra. And it's miracle that we can solve it via finding all eigenvalues.

In general there are several algorithms:

https://www-old.math.gatech.edu/academic/courses/core/math2601/Web-notes/5num.pdf

http://cstl-csm.semo.edu/jwojdylo/MA345/Chapter6/qrmethod/qrmethod.pdf

But they don't solve "full spectral problem". But looks that John Francis and Vera Kublanovskaya solved it. (Even I'm familiar only with basic QR algorithm which works only with real eigenvalues)

https://en.wikipedia.org/wiki/Vera_Kublanovskaya

https://www.quora.com/What-are-the-top-10-algorithms-of-the-20th-century