On hybrid addition of matrices

Mitra, Sujit Kumar ; Trapp, George E. (1975) On hybrid addition of matrices Linear Algebra and its Applications, 10 (1). pp. 19-35. ISSN 0024-3795

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Official URL: http://linkinghub.elsevier.com/retrieve/pii/002437...

Related URL: http://dx.doi.org/10.1016/0024-3795(75)90091-9


The definition of the hybrid sum of arbitrary matrices is given, and it is shown that this definition generalizes the previous work done for the hybrid sum of Hermitian positive semidefinite matrices. It is shown that hybrid summability of two matrices is equivalent to the consistancy of set of linear equations. These equations are then used to derive many properties of the hybrid sum, in particular commutativity and associativity. The shorted operator and matrix gyration are generalized and their relationship to hybrid addition is discussed.

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