Titlebook: Algebra; Serge Lang Textbook 2002Latest edition Springer Science+Business Media New York 2002 Algebra Textbook.Category theory.Textbook.al

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Representation of One Endomorphism Jordan canonical form for a representing matrix, which has a particularly simple shape when . is algebraically closed. This leads to a discussion of eigenvalues and the characteristic polynomial. The main theorem can be viewed as giving an example for the general structure theorem of modules over a

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Structure of Bilinear Forms theorems giving normalized expressions for these forms with respect to suitable bases. The chapter also follows the standard pattern of decomposing an object into a direct sum of simple objects, insofar as possible.

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The Tensor Productng multilinear maps, called the tensor product. We derive its basic properties, and postpone to Chapter XIX the special case of alternating products. The tensor product derives its name from the use made in differential geometry, when this product is applied to the tangent space or cotangent space o

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