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.