Titlebook: Linear Algebra; Larry Smith Textbook 1998Latest edition Springer Science+Business Media New York 1998 Eigenvalue.Eigenvector.Lineare Algeb

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The Elements of Vector Spaces: A Summing Up,The purpose of this chapter is twofold: to work out a number of numerical examples to illustrate and illuminate the portion of the theory of vector spaces we have developed so far, and to extend the theory in several different directions.

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Linear Transformations and Matrices,In this chapter we will begin the study of matrices, which are the analogue for linear transformations of coordinates for vectors. Our approach will be to consider first the case of a linear transformation.in some detail and then abstract the salient features to the general case. This leads to an agebra for matrices, which we then pursue further.

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Representing Linear Transformations by Matrices,In this chapter we return to the ideas we introduced in Chapter 10 to represent a linear transformation . : ?. → ?. by a 3 x 3 matrix. There is, of course, nothing sacred about ?. and its standard basis, and we will show that these ideas have far wider applications.

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