منابع مشابه
LINEAR ALGEBRA AND ITS APPLICATIONS Bound Norms
Recently Daniel and Palmer [2J have given an interesting application of a little-known lemma due to A. E. Taylor** [3J concerning the existence of an "orthogonal" basis for a finite dimensional (real or complex) normed vector space. Here we shall apply Taylor's lemma to obtain some simple results which have apparently not been noticed before. Thus we shall show that, given any bound norm (3, we...
متن کاملThe balanced truncation error bound in Schatten norms
The first main result in this article provides an error bound for balanced truncation where the matrix norm used is a general Schatten norm rather than the usual operator norm. The second main result in this article is that for the Schatten 1-norm (the trace class norm) this bound, for systems with a semi-definite Hankel operator, is in fact an equality. This class of systems for which we obtai...
متن کاملCorrespondence between probabilistic norms and fuzzy norms
In this paper, the connection between Menger probabilistic norms and H"{o}hle probabilistic norms is discussed. In addition, the correspondence between probabilistic norms and Wu-Fang fuzzy (semi-) norms is established. It is shown that a probabilistic norm (with triangular norm $min$) can generate a Wu-Fang fuzzy semi-norm and conversely, a Wu-Fang fuzzy norm can generate a probabilistic norm.
متن کاملActions, Norms, Subactions and Kernels of (Fuzzy) Norms
In this paper, we introduce the notion of an action $Y_X$as a generalization of the notion of a module,and the notion of a norm $vt: Y_Xto F$, where $F$ is a field and $vartriangle(xy)vartriangle(y') =$ $ vartriangle(y)vartriangle(xy')$ as well as the notion of fuzzy norm, where $vt: Y_Xto [0, 1]subseteq {bf R}$, with $bf R$ the set of all real numbers. A great many standard mappings on algebr...
متن کاملOn the Characterization of Least Upper Bound Norms in Matrix Space
of the origin in C ' , and vice versa. But clearly, not every convex compact neighbourhood of the origin in C ~' belongs to a lub norm. The principal problem to be considered here is the geometric characterizat ion of those convex bodies in C ~' which are associated with lub norms. The question arises because of the fact tha t m a n y of the properties of vector norms fall quite easily and natu...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1970
ISSN: 0024-3795
DOI: 10.1016/0024-3795(70)90024-8