These two papers discuss the notion of a matrix-based accounting system:
- Stewart A. Leech, The Theory and Development of a Matrix-Based Accounting System
- Robert A. Nehmer and Derek Robinson, An algebraic model for the representation of accounting systems
The first paper provides an example based on three transactions. Here are the transactions:
I created a prototype of a matrix represented using the XBRL technical syntax. I modeled those three transactions:
- XBRL Instance
- XBRL taxonomy schema
- Human readable (presentation relations) (XML Infoset of the same information)
- XBRL Cloud Evidence Package
Here is a good human readable rendering of the information in the XBRL instance:
(Click image for a larger view)
You can create exactly the same sort of XBRL instance using typed members rather than explicit members which might be a good idea because the chart of accounts would likely be potentially large and quite variable. You can assign properties to the [Member]s of the Debit [Axis] and Credit [Axis]. Interesting stuff.