Linear Algebra as a Balance Sheet

 

The matrix below is the accounting balance sheet of the future. It is a two-dimensional table like those found in the linear algebra branch of mathematics.. Each element of the matrix is a vector from an account that is credited to an account that is debited (the use of capital letters is preferred for this abstract demonstration over the more concrete names such as “Cash” or “Accumulated Depreciation”). Each vector is consistent with the use of a credited account as the origin of the transferred resource and the a debited account as its destination. This modern balance sheet contains all the information found in the traditional balance sheet, but it also contains an order of magnitude more information. This matrix of vectors is explained further in my book, “The Tao of Financial Information.” 

 

Accounts	A Credits	B Credits	C Credits	D Credits	E Credits	Debit Totals
A Debits	0	to A from B	to A from C	to A from D	to A from E	A Debit Total
B Debits	to B from A	0	to B from C	to B from D	to B from E	B Debit Total
C Debits	to C from A	to C from B	0	to C from D	to C from E	C Debit Total
D Debits	to D from A	to D from B	to D from C	0	to D from E	D Debit Total
E Debits	to E from A	to E from B	to E from C	to E from D	0	E Debit Total
Credit Totals	A Credit Total	B Credit Total	C Credit Total	D Credit Total	E Credit Total	0

 

The current conventional balance sheet is very primitive and is based on the traditions and mathematics of the historical medieval period, a time when western civilization was first using Arabic numbers and did not believe that negative numbers existed. The accounting analysis of the future can be found in the practice of linear algebra.