Results 31 to 40 of about 572 (50)
The Nullity Theorem for Principal Pivot Transform
, 2013 We generalize the nullity theorem of Gustafson [Linear Algebra Appl. (1984)] from matrix inversion to principal pivot transform. Several special cases of the obtained result are known in the literature, such as a result concerning local complementation ...
Brijder, Robert
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Lineability and modes of convergence [PDF]
, 2020 In this paper we look for the existence of large linear and algebraic structures of sequences of measurable functions with different modes of convergence. Concretely, the algebraic size of the family of sequences that are convergent in measure but not a.
Calderón Moreno, María del Carmen +2 more
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Possible numbers of x’s in an {x, y}-matrix with a given rank
Open Mathematics, 2017 Let x, y be two distinct real numbers. An {x, y}-matrix is a matrix whose entries are either x or y. We determine the possible numbers of x’s in an {x, y}-matrix with a given rank. Our proof is constructive.
Ma Chao
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On the Principal Permanent Rank Characteristic Sequences of Graphs and Digraphs
, 2015 The principal permanent rank characteristic sequence is a binary sequence $r_0 r_1 \ldots r_n$ where $r_k = 1$ if there exists a principal square submatrix of size $k$ with nonzero permanent and $r_k = 0$ otherwise, and $r_0 = 1$ if there is a zero ...
Horn, Paul +5 more
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Bilinear characterizations of companion matrices
Special Matrices, 2014 Companion matrices of the second type are characterized by properties that involve bilinear maps.
Lin Minghua, Wimmer Harald K.
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Minor-closed classes of binary functions [PDF]
Discrete Mathematics & Theoretical Computer ScienceBinary functions are a generalisation of the cocircuit spaces of binary matroids to arbitrary functions. Every rank function is assigned a binary function, and the deletion and contraction operations of binary functions generalise matroid deletion and ...
Benjamin R. Jones
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On relationships between two linear subspaces and two orthogonal projectors
Special Matrices, 2019 Sum and intersection of linear subspaces in a vector space over a field are fundamental operations in linear algebra. The purpose of this survey paper is to give a comprehensive approach to the sums and intersections of two linear subspaces and their ...
Tian Yongge
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Counting Semilinear Endomorphisms Over Finite Fields [PDF]
, 2011 For a finite field k and a triple of integers g \ge r \ge s \ge 0, we count the number of semilinear endomorphisms of a g-dimensional k-vector space which have rank r and stable rank s. Such endomorphisms show up naturally in the classification of finite
Holland, Timothy
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Families of graphs with maximum nullity equal to zero forcing number
Special Matrices, 2018 The maximum nullity of a simple graph G, denoted M(G), is the largest possible nullity over all symmetric real matrices whose ijth entry is nonzero exactly when fi, jg is an edge in G for i =6 j, and the iith entry is any real number.
Alameda Joseph S. +7 more
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Singular matrices possessing the triangle property
Special MatricesIt is known that the inverse of an invertible real square matrix satisfying the triangle property is a tridiagonal matrix. In this note, results that may be considered as analogues of this assertion are obtained for the Moore-Penrose inverse and the ...
Priya K. Kranthi, Sivakumar K. C.
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