Hi, I was wondering if anyone can point me in the right direction to understanding determinants. I don't want to know how to evaluate them. I want to know why they are evaluated the way they are. I want to know how they were derived and what the answers mean. Any links or replies regarding this topic would be great. I have been unable to find any information on this strangely.
Thank you for all the information. I realize now I need to develop a strong knowledge in concrete mathematics before continuing to try to understand. I'm weak on the mathematical notations so it makes it hard to understand. At least now I have access to information on determinants, so I thank you all for that.
I do own Shilov's book on Linear Algebra (well-written indeed), but I had trouble finding if he included the derivation of determinants or not. Whether or not it is revealed later in the book or I misread, I should still probably read on concrete mathematics before continuing.
If by derivation you mean motivation, then no, Shilov gives none. I think on something like page 3 or 4 he just throws at you the general determinant formula in all its glory.
The book I linked you to, Linear Algebra Done Wrong, motivates this definition by considering the "volume" formed by n vectors, each with n components (I quickly skimmed awkward's link and it looks similar). From this, Shilov's mysterious definition emerges and I agree with Drexel; I haven't seen a better treatment of determinants than Shilov's.