Theorems on ascent, descent, nullity and defect of linear operators
Theorems on ascent, descent, nullity and defect of linear operators
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DOI：
10.1007/bf02052483
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发表时间：
1966-02
影响因子：
1.4
通讯作者：
Angus E. Taylor
中科院分区：
文献类型：
--
作者：
Angus E. Taylor
Before I undertake to explain the nature of this paper I shall define the terms which occur in the title.Let X and Y be linear spaces over the field of complex numbers.(For many of the results the field could just as well be the field of real numbers. In dealing with spectral theory, however, we shall need the complex numbers.) Let T be a linear mapping with domain~(T) in X and range~(T) in Y. The null manifold of T, denoted by JV (T), is the set {x: x C~(T) and Tx= 0}. The dimension of~(T) is denoted by n (T); we call this the nullity of T. The dimension of the quotient space Y]~(T) is called the de/ect of T; it is denoted by d (T). In general, the dimension of a linear manifold M is denoted by dim M; it is 0 if M=(0), a positive integer p if M contains p, but not more than lo, linearly independent elements. Otherwise, M is not finite. dimensional and we write dim M= co.
