title: A group matrix representation relevant to scales of measurement of clinical disease states via stratified vectors.
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.
authors: Department of Psychiatry, Tokyo Women's Medical University, Tokyo, Japan. sawamura.jitsuki@twmu.ac.jp.
authors: Jitsuki
authors: J
authors: Sawamura
authors: Depression Prevention Medical Center, Inariyama Takeda Hospital, Kyoto, Japan. s.morishita69@mopera.net.
authors: Shigeru
authors: S
authors: Morishita
authors: Department of Psychiatry, Tokyo Women's Medical University, Tokyo, Japan. ishigooka.jun@twmu.ac.jp.
authors: Jun
authors: J
authors: Ishigooka
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D004194:Disease; D006801:Humans; D008433:Mathematics; D008962:Models, Theoretical; D012720:Severity of Illness Index