Permuted graph matrices and their applications
نویسنده
چکیده
A permuted graph matrix is a matrix V ∈ C(m+n)×m such that every row of the m×m identity matrix Im appears at least once as a row of V . Permuted graph matrices can be used in some contexts in place of orthogonal matrices, for instance when giving a basis for a subspace U ⊆ Cm+n, or to normalize matrix pencils in a suitable sense. In these applications the permuted graph matrix can be chosen with bounded entries, which is useful for stability reasons; several algorithms can be formulated with numerical advantage with permuted graph matrices. We present the basic theory and review some applications from optimization or in control theory.
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