Results 11 to 20 of about 8,210 (289)
A unification of unitary similarity transforms to compressed representations [PDF]
Numerische Mathematik, 2011 The authors propose algorithms which rely on the \(QR\)-factorization of the involved matrices. Even though using the \(QR\)-factorization for Hessenberg (H) matrices seems redundant, for many classes of structured rank matrices it provides means for a compact representation.
Raf Vandebril, Gianna M. Del Corso
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On unitary similarity of matrices
Linear Algebra and its Applications, 1989 The authors give a test for two \(n\times n\) nonsingular matrices with n distinct singular values to be unitarily similar. This depends on the equivalence of the traces of certain polynomials in the matrices and their adjoints. They remark that the method of proof can be extended to cover the situation when the matrices are singular and the nonzero ...
Bhattacharya, Ratna, Mukherjea, Kalyan
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Arveson’s criterion for unitary similarity
Linear Algebra and its Applications, 2011 This paper is an exposition of W.B. Arveson's complete invariant for the unitary similarity of complex, irreducible matrices.
Douglas Farenick, Farenick, Douglas
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Unitary automorphisms of the space of Toeplitz-plus-Hankel matrices
Special Matrices, 2015 Our motivation was a paper of 1991 indicating three special unitary matrices that map Hermitian Toeplitz matrices by similarity into real Toeplitz-plus-Hankel matrices.
Abdikalykov A.K. +2 more
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The Gerschgorin discs under unitary similarity [PDF]
Banach Center Publications, 1997 The intersection of the Gerschgorin regions over the unitary similarity orbit of a given matrix is studied. It reduces to the spectrum in some cases: for instance, if the matrix satisfies a quadratic equation, and also for matrices having “large” singular values or diagonal entries. This leads to a number of open questions. 1.
Zalewska-Mitura, A, Zemanek, J
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Transformations to rank structures by unitary similarity [PDF]
Linear Algebra and its Applications, 2005 Let \(A\) be a complex \(n\times n\) matrix. A Krylov matrix of \(A\) is a matrix of the form \(K:=\left[ v,Av,...,A^{n-1}v\right] \) for some column vector \(v\). If \(A\) is nonderogatory, then \(v\) can be chosen so that \(K\) is nonsingular; in this case \(K^{-1}AK\) is equal to the Frobenius (companion) matrix for \(A\). A matrix \(L=\left[ l_{ij}\
BEVILACQUA, ROBERTO +2 more
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Unitary similarity to a normal matrix
Linear Algebra and its Applications, 2012 The author gives several criteria of unitary similarity of a normal matrix \(A\) and any matrix \(B\) in terms of the Frobenius and spectral norms, characteristic polynomials, and traces of matrices.
Gerasimova, Tatiana G.
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On the Use of Lie Group Homomorphisms for Treating Similarity Transformations in Nonadiabatic Photochemistry [PDF]
Advances in Mathematical Physics, 2014 A formulation based on Lie group homomorphisms is presented for simplifying the treatment of unitary similarity transformations of Hamiltonian matrices in nonadiabatic photochemistry. A general derivation is provided whereby it is shown that a similarity
Benjamin Lasorne
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Antidiagonals of matrices in a unitary similarity orbit
Linear Algebra and its Applications, 1994 In the context of this paper, an antidiagonal of a matrix is a vector of matrix elements, running from the first column to the first row, at right angles to the main diagonal. A given \(n \times n\) matrix has one antidiagonal of length \(k\) for each \(k = 1, 2,\dots,n\).
Li, Chi-Kwong, Miranda, Maria Emília
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A survey of canonical forms and invariants for unitary similarity
Linear Algebra and its Applications, 1991 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Shapiro, Helene
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