August 14, 2008

The identity matrix: Semiotics or mathematical theory?

Based on the definition from Wikipedia –, an identity matrix can be defined as follows:

“In linear algebra, the identity matrix or unit matrix of size n is the n-by-n square matrix with ones on the main diagonal and zeros elsewhere. It is denoted by In, or simply by I if the size is immaterial or can be trivially determined by the context. (In some fields, such as quantum mechanics, the identity matrix is denoted by a boldface one, 1; otherwise it is identical to I.)

The identity matrix also has the property that, when it is the product of two square matrices, the matrices can be said to be the inverse of one another."

The names of other matrices in matrix algebra all make sense and are easily defined (e.g. square matrix, upper/lower triangular matrix, diagonal matrix, tridiagonal matrix, diagonally dominant matrix), yet the identity matrix seems to be embedded in a deeper symbolic and/or cultural meaning. What would Jung have said about this as an archetype?

Which mathematician named this particular kind of matrix an “ identity matrix" – and why don’t other matrices bear more interesting and culturally symbolic names?