Linear Algebra pp 307-341 | Cite as

The Spectral Theorem and Quadratic Forms

  • Larry Smith
Part of the Undergraduate Texts in Mathematics book series (UTM)


So far in our study of linear transformations we have concentrated on trying to find conditions that assure that the matrix of the transformation has a particular form. We have not asked the related question what are the properties of those transformations whose matrices are assumed to have a particularly simple form. 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 matrices are symmetric. We would therefore like to introduce the following:


Quadratic Form Orthonormal Basis Linear Transformation Real Root Product Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Springer Science+Business Media New York 1998

Authors and Affiliations

  • Larry Smith
    • 1
  1. 1.Mathematisches InstitutUniversität GöttingenGottingenGermany

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