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Titlebook: Linear Algebra; Werner Greub Textbook 1975Latest edition Springer Science+Business Media New York 1975 Matrix.algebra.automorphism.field.l

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发表于 2025-3-21 19:02:04 | 显示全部楼层 |阅读模式
书目名称Linear Algebra
编辑Werner Greub
视频video
丛书名称Graduate Texts in Mathematics
图书封面Titlebook: Linear Algebra;  Werner Greub Textbook 1975Latest edition Springer Science+Business Media New York 1975 Matrix.algebra.automorphism.field.l
描述This textbook gives a detailed and comprehensive presentation of linear algebra based on an axiomatic treatment of linear spaces. For this fourth edition some new material has been added to the text, for instance, the intrinsic treatment of the classical adjoint of a linear transformation in Chapter IV, as well as the discussion of quaternions and the classifica­ tion of associative division algebras in Chapter VII. Chapters XII and XIII have been substantially rewritten for the sake of clarity, but the contents remain basically the same as before. Finally, a number of problems covering new topics-e.g. complex structures, Caylay numbers and symplectic spaces - have been added. I should like to thank Mr. M. L. Johnson who made many useful suggestions for the problems in the third edition. I am also grateful to my colleague S. Halperin who assisted in the revision of Chapters XII and XIII and to Mr. F. Gomez who helped to prepare the subject index. Finally, I have to express my deep gratitude to my colleague J. R. Van­ stone who worked closely with me in the preparation of all the revisions and additions and who generously helped with the proof reading.
出版日期Textbook 1975Latest edition
关键词Matrix; algebra; automorphism; field; linear algebra; matrices; transformation; matrix theory
版次4
doihttps://doi.org/10.1007/978-1-4684-9446-4
isbn_softcover978-1-4684-9448-8
isbn_ebook978-1-4684-9446-4Series ISSN 0072-5285 Series E-ISSN 2197-5612
issn_series 0072-5285
copyrightSpringer Science+Business Media New York 1975
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Theory of a linear transformation, . be the minimum polynomial of .. Since .(.) is non-trivial and has finite dimension, it follows that deg . ≧ 1 (cf. sec. 12.11). The minimum polynomial of the zero transformation is . whereas the minimum polynomial of the identity map is .-1.
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https://doi.org/10.1007/978-1-4684-9446-4Matrix; algebra; automorphism; field; linear algebra; matrices; transformation; matrix theory
发表于 2025-3-22 18:46:10 | 显示全部楼层
Linear Mappings,Suppose . are vector spaces and let .: . be a linear mapping. Then the . of ., denoted by ker ., is the subset of vectors . such that . = 0. It follows from (1.8) and (1.9) that ker . is a subspace of ..
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Algebras,An ., is a vector space together with a mapping . × . such that the conditions (.) and (.) below both hold. The image of two vectors ., under this mapping is called the . of . and . and will be denoted by ..
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