Titlebook: Lectures in Abstract Algebra; II. Linear Algebra Nathan Jacobson Textbook 1953 The Editor(s) (if applicable) and The Author(s) 1953 Calcula

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The Theory of a Single Linear Transformation,paces into so-called cyclic subspaces relative to a given linear transformation. By choosing appropriate bases in these spaces we obtain certain canonical matrices for the transformation. These results yield necessary and sufficient conditions for similarity of matrices. Following Krull we shall der

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Sets of Linear Transformations,y of these notions belongs more properly to the so-called theory of representations of rings and is beyond the scope of the present volume. An introduction to these notions will serve to put into better perspective the results of the preceding chapter. We shall also be able to extend some of these r

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Bilinear Forms, vector space R and. is in a right vector space R′. The values of .(.,.) are assumed to belong to Δ, and the functions of one variable ..(.) = .(.,.) and ..(.) = .(.,.) obtained by fixing the other variable are linear. Of particular interest are the non-degenerate bilinear forms. These determine 1–1

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978-1-4684-7055-0The Editor(s) (if applicable) and The Author(s) 1953

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Graduate Texts in Mathematicshttp://image.papertrans.cn/l/image/583440.jpg

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Linear Transformations,elation between linear transformations and matrices is discussed. Also we define rank and nullity for arbitrary linear transformations. Finally we study a special type of linear transformation called a projection, and we establish a connection between transformations of this type and direct decompositions of the vector space.