3 ms·
Looks like a nice paper! The paper says how to go beyond what is in Boyd, et al., i.e., eigenvalues, eigenvectors, the spectral decomposition, etc. without det
by graycat 8y ago
Looks like a nice paper!
The paper says how to go beyond what is in Boyd, et al., i.e., eigenvalues, eigenvectors, the spectral decomposition, etc. without determinants. Nice!
For that material I would have been tempted just to use the old approach of determinants and the roots of the characteristic polynomial, the Hamilton-Cayley theoem, etc.
Saved the paper! Thx.
- selimthegrim 8y agoAnd if you really really love determinants there's https://www.amazon.com/Discriminants-Resultants-Multidimensional-Determinants-Birkhäuser-ebook/dp/B00F5QEH0I/ https://www.amazon.com/Discriminants-Resultants-Multidimensi... (warning: not for undergraduates)
- graycat 8y agoThere is also the chapter in P. Halmos, Finite Dimensional Vector Spaces on multi-linear algebra which at the time I read it I took it as an abstract approach to determinants, maybe also a start on exterior algebra of differential forms, but maybe there's a long shot chance that that Halmos chapter is related to multi-dimensional determinants. Can't read ALL the books on the shelves of the research libraries or even all the recent ones so have to be selective, to focus or as a startup entrepreneur before spending hundreds of hours in such a book (hope the author got tenure) ask "Why should I?".
- selimthegrim 8y agoI am sure Gelfand, Kapranov and Zelevinsky given their other math accomplishments all got tenure track positions when they emigrated. Will give Halmos another look.
- graycat 8y agoThat can't still be THE Gel'fand, along with Kolmogorov, prof of E. Dynkin? Must be a great grand son or some such.
- selimthegrim 8y agoHe passed recently, but yes it’s that one. The book is from 1994 and the research is from just before USSR fell.