In this short note, we introduce a class of orthogonal matrices of order n for which the matrix by vector product can be be computed in O(nlogn) instead o fO(n2). The matricesin this class form a proper Lie subgroup of the set of the orthogonal matrices random generatedfollowing the Haar’s measure distribution. Given a vector that has the absolute values of its entriespresenting large variations of magnitude, the product of a matrix in the subgroup by this vector willproduce a new vector where the magnitude of the absolute values of the entries does not vary by avery large amount.

Tensor product of random orthogolal matrices

Arioli M
2013

Abstract

In this short note, we introduce a class of orthogonal matrices of order n for which the matrix by vector product can be be computed in O(nlogn) instead o fO(n2). The matricesin this class form a proper Lie subgroup of the set of the orthogonal matrices random generatedfollowing the Haar’s measure distribution. Given a vector that has the absolute values of its entriespresenting large variations of magnitude, the product of a matrix in the subgroup by this vector willproduce a new vector where the magnitude of the absolute values of the entries does not vary by avery large amount.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12572/5935
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