Linear transformations which preserve or decrease rank
نویسندگان
چکیده
منابع مشابه
Curvature Element Transformations Which Preserve Integrable Fields.
I Shohat, J., Bull. Am. Math. Soc., 41, 51 (1935). 2 Haar, A., Math. Ann., 78, 121-136 (1918). 3 Young, W. H., Comptes Rendus, 165, 696-699 (1917). 4Szego, G., Math. Zeit., 12, 61-94 (1922). b A general treatment, which sets forth necessary and sufficient conditions for equivalence of expansions in terms of orthogonal functions, is given by Walsh, J. L., and Wiener, N., Jour. Math. and Phys. of...
متن کاملLinear Operators Which Preserve Pairs on Which the Rank Is Additive
Let A and B be m n matrices. A linear operator T preserves the set of matrices on which the rank is additive if rank(A + B) = rank(A) + rank(B) implies that rank(T (A) + T(B)) = rankT (A) + rankT (B). We characterize the set of all linear operators which preserve the set of pairs of n n matrices on which the rank is additive.
متن کاملDo Linear Transformations Preserve Fuzzy Linear Independence? Some Examples
In this paper, we examine whether basic linear transformations in R 2, such as rotations, scales, etc, preserve fuzzy linear independence. We provide some examples to the contrary. Mathematics Subject Classification: 08A72, 03E72
متن کاملLineal Element Transformations Which Preserve the Dual-Isothermal Character.
THEOREM. In order that a system S of o I curves represents the additivemultiplicative trajectories ofa given field, it is necessary (but not sufficient) that S possesses the dynamical Property I; this may be stated simply in either of these alternative geometric forms: Property Ia: For the o I curves of S passing through any lineal element E of the plane, construct the osculating parabolas at E...
متن کاملGraph Transformations Which Preserve the Multiplicity of an Eigenvalue
Graph transformations which preserve the multiplicity of the eigenvalue zero in the spectrum are known since 1970s and are of importance in chemical applications. We now show that analogous transformations hold for all graph eigenvalues that are of the form 2 cos rn, where Y is a rational number, 0 < r < 1.
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: 1989
ISSN: 0024-3795
DOI: 10.1016/0024-3795(89)90698-8