The Spectral Theorem and Quadratic Forms
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:
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