
Schur decomposition of several matrices
Schur decompositions and the corresponding Schur forms of a single matri...
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Simultaneous Diagonalization of Incomplete Matrices and Applications
We consider the problem of recovering the entries of diagonal matrices {...
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Orthogonal and Idempotent Transformations for Learning Deep Neural Networks
Identity transformations, used as skipconnections in residual networks,...
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A variant of Schur's product theorem and its applications
We show the following version of the Schur's product theorem. If M=(M_j,...
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Surjectivity of near square random matrices
We show that a nearly square iid random integral matrix is surjective ov...
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Efficient coordinatedescent for orthogonal matrices through Givens rotations
Optimizing over the set of orthogonal matrices is a central component in...
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On Transitive Consistency for Linear Invertible Transformations between Euclidean Coordinate Systems
Transitive consistency is an intrinsic property for collections of linea...
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Simultaneous hollowisation, joint numerical range, and stabilization by noise
We consider orthogonal transformations of arbitrary square matrices to a form where all diagonal entries are equal. In our main results we treat the simultaneous transformation of two matrices and the symplectic orthogonal transformation of one matrix. A relation to the joint real numerical range is worked out, efficient numerical algorithms are developped and applications to stabilization by rotation and by noise are presented.
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