Displaying similar documents to “The space of all bounded operators on Hilbert space does not have the approximation property”

An introduction to hierarchical matrices

Wolfgang Hackbusch, Lars Grasedyck, Steffen Börm (2002)

Mathematica Bohemica

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We give a short introduction to a method for the data-sparse approximation of matrices resulting from the discretisation of non-local operators occurring in boundary integral methods or as the inverses of partial differential operators. The result of the approximation will be the so-called hierarchical matrices (or short ℋ -matrices). These matrices form a subset of the set of all matrices and have a data-sparse representation. The essential operations for these matrices (matrix-vector...

Ranks of permutative matrices

Xiaonan Hu, Charles R. Johnson, Caroline E. Davis, Yimeng Zhang (2016)

Special Matrices

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A new type of matrix, termed permutative, is defined and motivated herein. The focus is upon identifying circumstances under which square permutative matrices are rank deficient. Two distinct ways, along with variants upon them are given. These are a special kind of grouping of rows and a type of partition in which the blocks are again permutative. Other, results are given, along with some questions and conjectures.