超线性代数
Super Linear Algebra
摘要：
在这本书中，作者介绍了概念的超级线性代数和超级向量空间使用的定义超级矩阵定义的霍斯特（1963年）。这本书期望读者精通线性代数。证明了关于超线性代数及其性质的许多定理。有些定理留给读者作练习.这类新的超线性代数可以看作是一组线性代数，在一定条件下，将在计算机上得到应用。作者认为，这种模式的转变是必不可少的，在这个计算机化的世界。一些其他的结构应该取代线性代数，这是一个多世纪的历史。使用超级矩阵的超级线性代数不仅可以将数据存储在一个块中，而且可以存储在多个块中，因此它肯定比通常的矩阵更强大。这本书有三章。第一章介绍了超向量空间的概念，并列举了一些性质。第二章定义了超线性代数、超内积空间和超双线性型的概念。几个有趣的属性派生。并给出了这些新结构在马尔可夫链和Leontief经济模型中的主要应用。最后一章提出了161个问题，主要是为了让读者理解这一新概念并加以应用。
英文摘要：
In this book, the authors introduce the notion of Super linear algebra and super vector spaces using the definition of super matrices defined by Horst (1963). This book expects the readers to be well-versed in linear algebra. Many theorems on super linear algebra and its properties are proved. Some theorems are left as exercises for the reader. These new class of super linear algebras which can be thought of as a set of linear algebras, following a stipulated condition, will find applications in several fields using computers. The authors feel that such a paradigm shift is essential in this computerized world. Some other structures ought to replace linear algebras which are over a century old. Super linear algebras that use super matrices can store data not only in a block but in multiple blocks so it is certainly more powerful than the usual matrices. This book has 3 chapters. Chapter one introduces the notion of super vector spaces and enumerates a number of properties. Chapter two defines the notion of super linear algebra, super inner product spaces and super bilinear forms. Several interesting properties are derived. The main application of these new structures in Markov chains and Leontief economic models are also given in this chapter. The final chapter suggests 161 problems mainly to make the reader understand this new concept and apply them.
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