# Defect

From Encyclopedia of Mathematics

*deficiency, deficiency number, of an operator*

The dimension $\dim D_\lambda$ of the deficiency subspace of the linear operator. Occasionally, in a wider sense, the deficiency of a linear manifold in a Hilbert space is defined to be the dimension of the orthogonal complement of this manifold.

**How to Cite This Entry:**

Defect.

*Encyclopedia of Mathematics.*URL: http://encyclopediaofmath.org/index.php?title=Defect&oldid=31947

This article was adapted from an original article by V.I. Sobolev (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article