منابع مشابه
Factoring Matrices into the Product of Circulant and Diagonal Matrices
A generic matrix A ∈ Cn×n is shown to be the product of circulant and diagonal matrices with the number of factors being 2n−1 at most. The demonstration is constructive, relying on first factoring matrix subspaces equivalent to polynomials in a permutation matrix over diagonal matrices into linear factors. For the linear factors, the sum of two scaled permutations is factored into the product o...
متن کاملAdding and multiplying random matrices: a generalization of Voiculescu's formulas.
In this paper, we give an elementary proof of the additivity of the functional inverses of the resolvents of large N random matrices, using recently developed matrix model techniques. This proof also gives a very natural generalization of these formulas to the case of measures with an external field. A similar approach yields a relation of the same type for multiplication of random matrices.
متن کاملAdding and multiplying random matrices: a generalization of Voiculescu’s formulae
In this paper, we give an elementary proof of the additivity of the functional inverses of the resolvents of large N random matrices, using recently developed matrix model techniques. This proof also gives a very natural generalization of these formulae to the case of measures with an external field. A similar approach yields a relation of the same type for multiplication of random matrices. 10...
متن کاملFactoring nonnegative matrices with linear programs
This paper describes a new approach for computing nonnegative matrix factorizations (NMFs) with linear programming. The key idea is a data-driven model for the factorization, in which the most salient features in the data are used to express the remaining features. More precisely, given a data matrix X , the algorithm identifies a matrix C that satisfies X ≈ CX and some linear constraints. The ...
متن کاملFactoring matrices with a tree-structured sparsity pattern
Article history: Received 12 May 2010 Accepted 15 March 2011 Available online xxxx Submitted by V. Mehrmann AMS classification: 65F50 65F05 15A23
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ژورنال
عنوان ژورنال: The American Mathematical Monthly
سال: 2018
ISSN: 0002-9890,1930-0972
DOI: 10.1080/00029890.2018.1408378