Thanks for the responses. However, I have a question.
Is the determinant uniquely determined by its multilinearity and the properties I mentioned above?
I am hoping that the determinant can be made into a type of analogue of the complex abosolute value with as few other conditions as possible...
How could one derive a definition of the determinant from some of its basic properties such as det of product = product of dets or the determinant of a transpose is the determinant of the untransposed matrix?
Upon instigating research on determiniants, all I've found are definitions that...
The proof that I have seen uses a bit of complex analysis on the contour integral found in Riemann's original paper. http://www.maths.tcd.ie/pub/HistMath/People/Riemann/Zeta/EZeta.pdf is a good translation (the integral is found in the middle of the third page).
The integrand there is a power...
The gauge integral (and is variations) includes the Lebesgue integral as a special case. It is equivalent for bounded functions on a finite interval. It can also integrate some unbounded functions and some functions that are not absolutely integrable. Its defintion is nearly as simple as the...