Title |
A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors
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Published in |
Theoretical Biology and Medical Modelling, February 2016
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DOI | 10.1186/s12976-016-0031-8 |
Pubmed ID | |
Authors |
Jitsuki Sawamura, Shigeru Morishita, Jun Ishigooka |
Abstract |
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. 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. 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. 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. |
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