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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Groups and Group Homomorphisms,ear algebra. In the early stages, the student will perhaps see only a rather arbitrary looking (but attractive!) informal axiomatic system. This is a gross deception. The definition distills millennia of mathematical experience. Another theme also emerges: objects are not nearly so interesting in th

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Vector Spaces and Linear Transformations,rbitrary, but as we shall see in subsequent chapters, they are a masterpiece of abstraction—general enough to admit a vast range of diverse particular instances, but restrictive enough to capture the fundamental geometric notion of dimension.

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Dimension,called .) and that the number of coordinates is intrinsic to the space. These results in turn allow us to define the . of a vector space and thus to recast this most basic of geometric notions in purely algebraic terms. In so doing, we extend the application of this concept to many settings that hav

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Matrices, any extrinsic meaning. We define the elements of matrix arithmetic and show that it is formally well behaved, which is surprising since the definition of matrix multiplication looks somewhat unnatural at this point. Second, we consider the connection between matrices and linear systems of equations

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Representation of Linear Transformations,ee that in a strong sense every linear transformation of finite-dimensional vector spaces over . may be thus realized. (We say that the associated matrix . 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 th

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Eigenvalues and Eigenvectors,-behaved, independent component subprocesses. What is especially noteworthy and exciting about the material is that it uses all of the major concepts introduced so far, including the representation of linear transformations, real and complex inner product spaces, and the theory of determinants. The

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