The 4 elements of a 2 by 2 matrix can be used to represent the 4 corners of a house facing directly east, west, north, and south as the NE, NW, SE, and SW corners. If NE=1, NW=1, SE=1, and SW=1 then the matrix is singular as well as symmetric and its determinant is zero. Moreover, any symmetric matrix of positive or negative unity elements also has determinant zero and its inverse cannot be defined using rules of mathematics. On the other hand, if differences exist such that NW-NE or NW-SW or SW-SE or NE-SE is not all identically zero then a unique inverse can be found.
The house rules for finding this unique inverse are as follows: the values of the NW and SE are negatively switched and the inverse matrix is multiplied by the reciprocal factor given by the product of the differences of NW-NE and NW-SW. With the exceptions, these rules fail miserably for finding the self-inverses of the positive or the negative identity matrix.


LinkBack URL
About LinkBacks
Reply With Quote

