Titlebook: Basic Linear Algebra; Thomas S. Blyth,Edmund F. Robertson Textbook 19981st edition Springer-Verlag London 1998 Eigenvalue.Eigenvector.Matr

分散

https://doi.org/10.1007/978-3-642-79107-9In what follows it will be convenient to write an . × . matrix A in the form . where, as before, .., represents the .-th column of .. Also, the letter . will signify either the field ?; of real numbers or the field ? of complex numbers.

Congruous

Sylvie Cabrit,Alex Raga,Frederic GuethIn Chapter 9 we introduced the notions of . and . of a matrix or of a linear mapping. There we concentrated our attention on showing the importance of these notions in solving particular problems. Here we shall take a closer algebraic look.

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外形

Some Applications of Matrices,We shall now give brief descriptions of some situations to which matrix theory finds a natural application, and some problems to which the solutions are determined by the algebra that we have developed. Some of these applications will be dealt with in greater detail in later chapters.

一美元

Systems of Linear Equations,We shall now consider in some detail a systematic method of solving systems of linear equations. In working with such systems, there are three basic operations involved:

字形刻痕

Invertible Matrices,In Theorem 1.3 we showed that every . matrix . has an additive inverse, denoted by ?A, which is the unique . × . matrix . that satisfies the equation . + . = 0. We shall now consider the multiplicative analogue of this.

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一致性

Linear Mappings,In the study of any algebraic structure there are two concepts that are of paramount importance. The first is that of a . (i.e. a subset with the same type of structure), and the second is that of a . (i.e. a mapping from one structure to another of the same kind that is ‘structure-preserving’).

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The Matrix Connection,We shall now proceed to show how a linear mapping from one finite-dimensional vector space to another can be represented by a matrix. For this purpose, we require the following notion.

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Determinants,In what follows it will be convenient to write an . × . matrix A in the form . where, as before, .., represents the .-th column of .. Also, the letter . will signify either the field ?; of real numbers or the field ? of complex numbers.