A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors. Issue 1 (December 2016)

• Record Type: Journal Article
• Authors: Sawamura, Jitsuki; Morishita, Shigeru; Ishigooka, Jun
• Is Part Of: Theoretical biology and medical modelling. Volume 13:Issue 1(2016)
• Page Start: 1
• Page End: 22
• Publication Date: 2016-12
• Subjects: Group -- Ring -- Operation -- Stratified vector -- Matrix representation -- Clinical medicine; Biology -- Mathematical models -- Periodicals; Biology -- Periodicals; Medical sciences -- Periodicals; 570.15118
• DOI: 10.1186/s12976-016-0031-8
• Languages: English
• ISSNs: 1742-4682

Abstract

Abstract 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 Rj (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 [Rj ]s. The [Rj ]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 [Rj ]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.