Generalized inverses with nonnegative principal minors
نویسندگان
چکیده
منابع مشابه
Singular Values and Maximum Rank Minors of Generalized Inverses
Singular values and maximum rank minors of generalized inverses are studied. Proportionality of maximum rank minors is explained in terms of space equivalence. The Moore–Penrose inverse A† is characterized as the {1}–inverse of A with minimal volume.
متن کاملOn Splittings of Matrices and Nonnegative Generalized Inverses
The authors introduce a new type of matrix splitting generalizing the notion of B splitting and study its relationships with nonnegativity of the Moore-Penrose inverse and the group inverse. Mathematics subject classification (2010): 15A09, 15B48.
متن کاملNonnegative Minors of Minor Matrices
Using the relationship between totally nonnegative matrices and directed acyclic weighted planar networks, we show that 2× 2 minors of minor matrices of totally nonnegative matrices are also nonnegative. We give a combinatorial interpretation for the minors of minor matrices in terms of the weights of families of paths in a network. Introduction By attaching weights to the edges of a finite, di...
متن کاملPrincipal minors and rhombus tilings
The algebraic relations between the principal minors of an n× n matrix are somewhat mysterious, see e.g. [LS09]. We show, however, that by adding in certain almost principal minors, the relations are generated by a single relation, the so-called hexahedron relation, which is a composition of six cluster mutations. We give in particular a Laurent-polynomial parameterization of the space of n× n ...
متن کاملGeneralized Inverses and Applications
Fredholm’s method to solve a particular integral equation in 1903, was probably the first written work on generalized inverses. In 1906, Moore formulated the generalized inverse of a matrix in an algebraic setting, which was published in 1920, and in the thirties von Neumann used generalized inverses in his studies of continuous geometries and regular rings. Kaplansky and Penrose, in 1955, inde...
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: 1988
ISSN: 0024-3795
DOI: 10.1016/0024-3795(88)90066-3