摘要翻译：
这篇文章致力于在遗传密码的矩阵表示中的对称和代数现象。研究了基于字母矩阵[C A；U G]的Kronecker族遗传矩阵，其中C,A,U,G是遗传字母表的字母。第三次Kronecker幂中的矩阵P=[Ca；Ug]是(8*8)-矩阵，它包含64个三元组。遗传密码退化的特点反映在64个三胞胎的遗传(8*8)矩阵的对称黑白镶嵌中。揭示了这种镶嵌矩阵（以及许多其他遗传矩阵）与投影算子的联系现象。考虑到投影算符在量子力学、数字编码理论、计算机科学、逻辑学等许多应用数学领域中的重要作用，我们研究了这些现象的代数性质和生物学意义。在此基础上，提出了有限维向量空间理论的概念和形式在生物信息学和理论生物学中的应用。
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英文标题：
《Matrix genetics, part 5: genetic projection operators and direct sums》
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作者：
Sergey V. Petoukhov
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最新提交年份：
2010
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分类信息：

一级分类：Quantitative Biology        数量生物学
二级分类：Other Quantitative Biology        其他定量生物学
分类描述：Work in quantitative biology that does not fit into the other q-bio classifications
不适合其他q-bio分类的定量生物学工作
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英文摘要：
  The article is devoted to phenomena of symmetries and algebras in matrix presentations of the genetic code. The Kronecker family of the genetic matrices is investigated, which is based on the alphabetical matrix [C A; U G], where C, A, U, G are the letters of the genetic alphabet. The matrix P=[C A; U G] in the third Kronecker power is the (8*8)-matrix, which contains 64 triplets. Peculiarities of the degeneracy of the genetic code are reflected in the symmetrical black-and-white mosaic of this genetic (8*8)-matrix of 64 triplets. Phenomena of connections of this mosaic matrix (and many other genetic matrices) with projection operators are revealed. Taking into account an important role of projection operators in quantum mechanics, theory of digital codes, computer science, logic and in many other fields of applied mathematics, we study algebraic properties and biological meanings of these phenomena. Using of notions and formalisms of theory of finite-dimensional vector spaces in bioinformatics and theoretical biology is proposed on the bases of the described results.
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PDF链接：
https://arxiv.org/pdf/1005.5101