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

Aprope

0072-5285 n familiarity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup­posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of t

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Euclidean and Unitary Spaces, is customary to denote it simply as (., .) instead of .(., .) as in the preceding chapter. The geometric meaning of (.) is clear. It gives the product of the cosine of the angle between . and . by the lengths of the two vectors. The length of . can also be expressed in terms of the scalar product, namely, |.| = (.,.).

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The Theory of a Single Linear Transformation,e in this chapter the Hamilton-Cayley Frobenius theorems on the characteristic and minimum polynomials of a matrix. Finally we study the algebra of linear transformations that commute with a given transformation.

Gesture

Products of Vector Spaces, Kronecker product of two vector spaces over a field. We also discuss the elements of tensor algebra, and we consider the extension of a vector space over a field Φ to a vector space over a field P containing Φ. Finally we consider the concept of a (non-associative) algebra over a field, and we define the direct product of algebras.

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Textbook 1953ity with the basic concepts treated in Volume I: groups, rings, fields, homomorphisms, is presup­posed. However, we have tried to make this account of linear algebra independent of a detailed knowledge of our first volume. References to specific results are given occasionally but some of the fundame

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