Journal•ISSN: 0308-1087
Linear & Multilinear Algebra
Taylor & Francis
About: Linear & Multilinear Algebra is an academic journal published by Taylor & Francis. The journal publishes majorly in the area(s): Matrix (mathematics) & Eigenvalues and eigenvectors. It has an ISSN identifier of 0308-1087. Over the lifetime, 4240 publications have been published receiving 42291 citations. The journal is also known as: Linear & multilinear algebra (Online) & Linear and multilinear algebra (CD-ROM).
Topics: Matrix (mathematics), Eigenvalues and eigenvectors, Rank (linear algebra), Numerical range, Hilbert space
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TL;DR: In this paper, Equalities and Inequalities for Ranks of Matrices are discussed in the context of linear and multilinear algebras with respect to rank matrices.
Abstract: (1974). Equalities and Inequalities for Ranks of Matrices. Linear and Multilinear Algebra: Vol. 2, No. 3, pp. 269-292.
701 citations
TL;DR: In this paper, the Laplacian matrix of a finite undirected graph G with no loops or multiple edges is defined and the structure of the graph G is related to the eigenvalues of A(G): in particular, it is shown that all eigen values of Δ(G) are non-negative, less than or equal to the number of vertices, and less than/or equal to twice the maximum vertex degree.
Abstract: Let G be a finite undirected graph with no loops or multiple edges. We define the Laplacian matrix of G,Δ(G)by Δij= degree of vertex i and Δij−1 if there is an edge between vertex i and vertex j. In this paper we relate the structure of the graph G to the eigenvalues of A(G): in particular we prove that all the eigenvalues of Δ(G) are non-negative, less than or equal to the number of vertices, and less than or equal to twice the maximum vertex degree. Precise conditions for equality are given.
495 citations
421 citations
TL;DR: The matrix M m,n is defined in this paper as the matrix having as rows, every nth row starting with the first row, then every Nth row beginning with the second row, and so on.
Abstract: The vec-permutation matrix I m,n is defined by the equation vec A m × n = I m,n vecA′, Where vec is the vec operator such that vecA is the vector of columns of A stacked one under the other. The variety of definitions, names and notations for I m,n are discussed, and its properties are developed by simple proofs in contrast to certain lengthy proofs in the literature that are based on descriptive definitions. For example, the role of I m,n in reversing the order of Kronecker products is succinctly derived using the vec operator. The matrix M m,n is introduced as M m,n = I m,n M; it is the matrix having as rows,every nth row starting with the first, then every nth row starting with the second, and so on. Special cases of M m,n are discussed.
346 citations
TL;DR: In this article, the notion of the core inverse is introduced as an alternative to the group inverse and several properties of its properties are derived with a perspective towards possible applications, such as matrix partial ordering.
Abstract: This article introduces the notion of the Core inverse as an alternative to the group inverse. Several of its properties are derived with a perspective towards possible applications. Furthermore, a matrix partial ordering based on the Core inverse is introduced and extensively investigated.
297 citations