= Operator theory
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Linear operator theory studies <linear maps>, their <spectra>, <invariant subspaces>, and normal forms such as <Jordan normal form>. In a <finite-dimensional vector space>, <eigenvalues> identify parameters for which a shifted <linear operator> cannot be inverted. In an <infinite-dimensional vector space>, inversion can fail even without an <eigenvector>. The <spectrum of a bounded operator> captures this larger obstruction and connects <linear algebra> with the approximation questions of <functional analysis>.
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