This paper presents a new technique for expressing rhotrices in a generalize form. The method involves using multiple array indexes as analogous to matrix expressions, unlike the earlier method in the literature, whic...This paper presents a new technique for expressing rhotrices in a generalize form. The method involves using multiple array indexes as analogous to matrix expressions, unlike the earlier method in the literature, which can only be functional in a single array computational environment. The new rhotrix look will encourage the study of rhotrix algebra and analysis from a better perspective. In addition, computing efficiency and accuracy will also be improved, particularly when the operations in rhotrix space over the new expression are algorithmatized for computing machines.展开更多
This paper considers rank of a rhotrix and characterizes its properties, as an extension of ideas to the rhotrix theory rhomboidal arrays, introduced in 2003 as a new paradigm of matrix theory of rectangular arrays. F...This paper considers rank of a rhotrix and characterizes its properties, as an extension of ideas to the rhotrix theory rhomboidal arrays, introduced in 2003 as a new paradigm of matrix theory of rectangular arrays. Furthermore, we present the necessary and sufficient condition under which a linear map can be represented over rhotrix.展开更多
This paper presents an up-to-date review of the developments made in the field of rhotrix theory for a decade, starting from the year 2003, when the concept of rhotrix was introduced, up to the end of 2013. Over forty...This paper presents an up-to-date review of the developments made in the field of rhotrix theory for a decade, starting from the year 2003, when the concept of rhotrix was introduced, up to the end of 2013. Over forty articles on rhotrix theory have been published in journals since its inception, indicating the need for a first review.展开更多
文摘This paper presents a new technique for expressing rhotrices in a generalize form. The method involves using multiple array indexes as analogous to matrix expressions, unlike the earlier method in the literature, which can only be functional in a single array computational environment. The new rhotrix look will encourage the study of rhotrix algebra and analysis from a better perspective. In addition, computing efficiency and accuracy will also be improved, particularly when the operations in rhotrix space over the new expression are algorithmatized for computing machines.
文摘This paper considers rank of a rhotrix and characterizes its properties, as an extension of ideas to the rhotrix theory rhomboidal arrays, introduced in 2003 as a new paradigm of matrix theory of rectangular arrays. Furthermore, we present the necessary and sufficient condition under which a linear map can be represented over rhotrix.
文摘This paper presents an up-to-date review of the developments made in the field of rhotrix theory for a decade, starting from the year 2003, when the concept of rhotrix was introduced, up to the end of 2013. Over forty articles on rhotrix theory have been published in journals since its inception, indicating the need for a first review.
