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Titlebook: Linear Algebra; An Introduction to A Robert J. Valenza Textbook 1993 Springer Science+Business Media New York 1993 Algebra.Eigenvalue.Eigen

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发表于 2025-3-21 17:11:07 | 显示全部楼层 |阅读模式
书目名称Linear Algebra
副标题An Introduction to A
编辑Robert J. Valenza
视频video
丛书名称Undergraduate Texts in Mathematics
图书封面Titlebook: Linear Algebra; An Introduction to A Robert J. Valenza Textbook 1993 Springer Science+Business Media New York 1993 Algebra.Eigenvalue.Eigen
描述Based on lectures given at Claremont McKenna College, this text constitutes a substantial, abstract introduction to linear algebra. The presentation emphasizes the structural elements over the computational - for example by connecting matrices to linear transformations from the outset - and prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.
出版日期Textbook 1993
关键词Algebra; Eigenvalue; Eigenvector; Matrix; Permutation; homomorphism; linear algebra; matrix theory
版次1
doihttps://doi.org/10.1007/978-1-4612-0901-0
isbn_softcover978-1-4612-6940-3
isbn_ebook978-1-4612-0901-0Series ISSN 0172-6056 Series E-ISSN 2197-5604
issn_series 0172-6056
copyrightSpringer Science+Business Media New York 1993
The information of publication is updating

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Groups and Group Homomorphisms,gross deception. The definition distills millennia of mathematical experience. Another theme also emerges: objects are not nearly so interesting in themselves as the relationships they bear to one another. In the case of groups, these relationships are expressed by group homomorphisms.
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Representation of Linear Transformations,rix . the transformation.) In passing, we introduce the notion of a . a rich structure that is a hybrid of both vector space and ring. We show that the set of linear transformations from an .-dimensional vector space to itself is in fact isomorphic as a .-algebra to the familiar matrix algebra .(.).
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Determinants,ent of uniqueness and a surprising multiplicative property. [The determinant turns out to be a group homomorphism from GL.(.) to ..] Finally, from this multiplicativity one easily deduces that a square matrix is invertible if and only if its determinant is not zero.
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Textbook 1993 the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.
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0172-6056 d prepares the student for further study of abstract mathematics. Uniquely among algebra texts at this level, it introduces group theory early in the discussion, as an example of the rigorous development of informal axiomatic systems.978-1-4612-6940-3978-1-4612-0901-0Series ISSN 0172-6056 Series E-ISSN 2197-5604
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