New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations a...New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.展开更多
In this paper, the concept of I-bornological vector spaces and two examples of the spaces are given. Two methods on constructing new I-bornological vector spaces are discussed,one is using a（crisp） bornological vect...In this paper, the concept of I-bornological vector spaces and two examples of the spaces are given. Two methods on constructing new I-bornological vector spaces are discussed,one is using a（crisp） bornological vector space to induce an I-bornological vector space, the other is utilizing I-bornological linear maps to generate an I-bornological vector space.展开更多
In this paper,the global and local linear independence of any compactly supported distributions by using time domain spaces,and of refinable vectors by invariant linear spaces are investigated.
In this short note we discuss the GM property of some special linear transformation pairs over infinite-dimensional vector spaces. In particular, it is proved that if R =- End（VD） is the endomorphism ring of an infi...In this short note we discuss the GM property of some special linear transformation pairs over infinite-dimensional vector spaces. In particular, it is proved that if R =- End（VD） is the endomorphism ring of an infinite-dimensional right vector space V over a division ring D with IC（D）I 〉 3 and g e R, then （a0q-alg, 9） is a GM pair for any ao, ale C（D）. Furthermore, two existing results are obtained as immediate consequences.展开更多
To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering course...To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering courses, the minimum contents required has been determined. Rules are proposed to meet the background of most freshman students. An application oriented, easy to understand, computer based text book “Applied Popular Linear Algebra with MATLAB” [1] was published.展开更多
文摘New objects characterizing the structure of complex linear transformations areintroduced. These new objects yield a new result for the decomposition of complexvector spaces relative to complex lrnear transformations and provide all Jordan basesby which the Jordan canonical form is constructed. Accordingly, they can result in thecelebrated Jordan theorem and the third decomposition theorem of space directly. and,moreover, they can give a new deep insight into the exquisite and subtle structure ofthe Jordan form. The latter indicates that the Jordan canonical form of a complexlinear transformation is an invariant structure associated with double arbitrary. choices.
基金Supported by the National Natural Science Foundation of China(Grant No.11301281)the Natural Science Foundation of Anhui Higher Education Institution(Grant No.KJ2012A136)
文摘In this paper, the concept of I-bornological vector spaces and two examples of the spaces are given. Two methods on constructing new I-bornological vector spaces are discussed,one is using a（crisp） bornological vector space to induce an I-bornological vector space, the other is utilizing I-bornological linear maps to generate an I-bornological vector space.
文摘In this paper,the global and local linear independence of any compactly supported distributions by using time domain spaces,and of refinable vectors by invariant linear spaces are investigated.
文摘In this short note we discuss the GM property of some special linear transformation pairs over infinite-dimensional vector spaces. In particular, it is proved that if R =- End（VD） is the endomorphism ring of an infinite-dimensional right vector space V over a division ring D with IC（D）I 〉 3 and g e R, then （a0q-alg, 9） is a GM pair for any ao, ale C（D）. Furthermore, two existing results are obtained as immediate consequences.
文摘To find out what knowledge in linear algebra is essential to non-mathematics students, a reverse tracking method was used. Based on practical problems likely to encountered by students in subsequent engineering courses, the minimum contents required has been determined. Rules are proposed to meet the background of most freshman students. An application oriented, easy to understand, computer based text book “Applied Popular Linear Algebra with MATLAB” [1] was published.
