Titlebook: Linear Algebra; Larry Smith Textbook 19781st edition Springer-Verlag, New York Inc. 1978 Eigenvalue.Eigenvector.Lineare Algebra.Vector spa

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胰臟

Matrices,In the last chapter we saw that a linear transformation . : ?. → ?. could be represented (that is, was completely determined by) 9 numbers arranged in a 3 × 3 array. In this chapter we will study such arrays, which are called matrices. We will return to the connection between matrices and linear transformations in the next chapter.

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More on representing linear transformations by matrices,Our purpose in this chapter is to develop further the theory and technique of representing linear transformations by matrices. We will touch on several scattered topics and techniques. It is to be emphasized that we are only scratching the surface of an iceberg!

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Systems of linear equations,In the historical development of linear algebra the geometry of linear transformations and the algebra of systems of linear equations played significant and important rolls.

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The elements of eigenvalue and eigenvector theory,Suppose that . is a linear transformation of the vector space . to itself. Such linear transformations have a special name (because their domain and range space are the same), they are called ..

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Inner product spaces,rtant parts in the further development of linear algebra and it is now time to introduce these ingredients into our study. There are many ways to do this and in the approach that we will follow both length and angle will be derived from a more fundamental concept called a . or . product of two vectors.

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The spectral theorem and quadratic forms,rm. There is in fact a good reason for this and it is tied up with our work of the last chapter. For example we might propose to study those linear transformations whose matrix is symmetric. We would therefore like to introduce the following: