Abstract
BackgroundPreviously, 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.MethodsStarting 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.ResultsThe 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.ConclusionsDespite 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.
Highlights
We applied basic group theory and related concepts to scales of measurement of clinical disease states and clinical findings
Clinical medicine has not attained a similar level of sophistication that would link it to the natural sciences
A composition of stratified vectors that separately expresses plural operations in individual components To visualize its behaviors, a group is often described as a linear combination of all matrix elements
Summary
We applied basic group theory and related concepts to scales of measurement of clinical disease states and clinical findings (including laboratory data). For much of the 20th century, abstract algebras such as groups and related structures, including rings, group rings, and fields, have been adopted in various fields of natural science [1,2,3,4,5]. In 1946, Stevens proposed four classifications of measurements: “Nominal”, “Ordinal”, “Interval” and “Ratio”. These categories have become widely used in the medical fields and have played important roles in constructing and interpreting scales [17]. We applied basic group theory and related
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