A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors

Background

Previously, we applied basic group theory and related concepts to scales of measurement of clinical disease states and clinical findings (including laboratory data). To gain a more concrete comprehension, we here apply the concept of matrix representation, which was not explicitly exploited in our previous work.

Methods

Starting with a set of orthonormal vectors, called the basis, an operator R_j (an N-tuple patient disease state at the j-th session) was expressed as a set of stratified vectors representing plural operations on individual components, so as to satisfy the group matrix representation.

Results

The stratified vectors containing individual unit operations were combined into one-dimensional square matrices R_j]s. The R_j]s meet the matrix representation of a group (ring) as a K-algebra. Using the same-sized matrix of stratified vectors, we can also express changes in the plural set of R_j]s. The method is demonstrated on simple examples.

Conclusions

Despite the incompleteness of our model, the group matrix representation of stratified vectors offers a formal mathematical approach to clinical medicine, aligning it with other branches of natural science.