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Advanced Mathematics for Applications by Andrea Prosperetti

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18

Matrices and Finite-Dimensional Linear Spaces

 

Matrix theory is a large subject which, among others, plays a central role in scientific computing. Here we will only deal with a few selected topics of direct relevance to classical field theory. In particular, we will focus on some aspects which are useful to illustrate the general ideas underlying the theory of linear operators, a topic which is taken up in Part III of this book.

It is next to impossible to discuss matrix theory without reference to the theory of linear vector spaces, which provides a deeper and ultimately much more illuminating view of the entire subject. We assume that the reader is familiar with the elementary aspects of this subject (finite-dimensional vectors, ...

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