Unitary Triangularization of a Nonsymmetric Matrix

By A. Householder. 1958

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Citations in the corpus

Sorting out Lipschitz function approximation (2018, methodology): “Other researchers [2, 53, 46] have explicitly parameterized square orthogonal weight matrices using, for example, Householder transformations [25].”
Full-Capacity Unitary Recurrent Neural Networks (2016, background): “Arjovsky et al. [10] propose the following parameterization of the unitary matrix W : where D are diagonal unitary matrices, R are Householder reﬂection matrices [11], F is a discrete Fourier transform (DFT) matrix, and P is a permutation matrix.”
Improving Variational Auto-Encoders using Householder Flow (2016, background): “Moreover, the Householder matrix Hk is orthogonal matrix itself [7].”
Kaleidoscope: An Efficient, Learnable Representation For All Structured Linear Maps (2020, methodology): “To do this, we consider the class of Householder reflections, given by I− 2uu∗ for any unit vector u (Householder, 1958): Lemma K.”
Eigenvalue computation in the 20th century (2000, background): “A few years later, Householder, in 1958 [63], discovered that complete columns of A could be reduced to zero, outside the tridiagonal part, by the more e cient Householder re ections.”
MIMO Transceiver Design via Majorization Theory (2007, unknown): “(c) The QR factorization [48, 67]”
Eigenvalue statistics for beta-ensembles (2003, methodology): “The bidiagonalization method is due to Golub and Kahan [34], while the tridiagonalization method is due to Householder [40].”
Calculating the singular values and pseudo-inverse of a matrix (2007, background): “The proof will be a constructive one in which Householder transformations (see [17], [21], [32]) are used.”
Stimulated Raman adiabatic passage in physics, chemistry, and beyond (2016, background): “48 (a), can produce a Householder reflection (Householder, 1958) in the subset on N lower states.”
Rational points on the unit sphere (2008, background): “(17) It is well known [14],[4] that, for some h ≤ n and some unit vectors u1,u2, .”