I learned double entry accounting. "Debits decrease and credits increase" is just one way to represent the numbers; I have also seen the other way around (where debits are positive). But more commonly, the presentation is such that debits increase the accounts on the left, and credits increase the accounts on the right. (Nevertheless, the explanation there does work.)

Some time ago (while I was bored in the accounting class), I invented "matrix accounting" (I was trying to invent something else, specifically, using complex numbers in accounting, which I concluded was impossible, but matrix math works). In this matrix accounting, "debits" and "credits" don't really exist and the presentations mentioned above are really just different eigenvectors. The accounting equation has this form:

  <BAL|FSV> = 0

(Note that all of the components here are real, and not complex; also note that financial vector space is a kind of projective space.)