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.
There 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?".
I am sure Gelfand, Kapranov and Zelevinsky given their other math accomplishments all got tenure track positions when they emigrated. Will give Halmos another look.
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.