Spectral Theory
نویسنده
چکیده
In many applications it is important to understand the spectral properties of a linear operator T : X → X, where X is some vector space over IR or I C. In the finite dimensional (complex) case linear operators may be characterised as matrices and the Jordan normal form theorem applies, providing a basis of generalised eigenvectors. If, in addition, T is normal (i.e. T and T ∗ commute) with respect to an inner product, then the basis is orthogornal and consists of eigenvectors only. For spectral theory it is often convenient to work in complex spaces. For symmetric operators however the real numbers are just fine. The simplest theorem for the infinite dimensional case may be formulated and proved in the real setting.
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