Scaling of symmetric matrices by positive diagonal congruence
نویسندگان
چکیده
منابع مشابه
Scaling-Rotation Distance and Interpolation of Symmetric Positive-Definite Matrices
We introduce a new geometric framework for the set of symmetric positive-definite (SPD) matrices, aimed at characterizing deformations of SPD matrices by individual scaling of eigenvalues and rotation of eigenvectors of the SPD matrices. To characterize the deformation, the eigenvalue-eigenvector decomposition is used to find alternative representations of SPD matrices and to form a Riemannian ...
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We give a constructive proof of a theorem of Marshall and Olkin that any real symmetric positive definite matrix can be symmetrically scaled by a positive diagonal matrix to have arbitrary positive row sums. We give a slight extension of the result, showing that given a sign pattern, there is a unique diagonal scaling with that sign pattern, and we give upper and lower bounds on the entries of ...
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Indefinite symmetric matrices that are estimates of positive definite population matrices occur in a variety of contexts such as correlation matrices computed from pairwise present missing data and multinormal based theory for discretized variables. This note describes a methodology for scaling selected off-diagonal rows and columns of such a matrix to achieve positive definiteness. As a contra...
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ژورنال
عنوان ژورنال: Linear and Multilinear Algebra
سال: 2009
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081080600872327