Scaling-Rotation Distance and Interpolation of Symmetric Positive-Definite Matrices
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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ژورنال
عنوان ژورنال: SIAM Journal on Matrix Analysis and Applications
سال: 2015
ISSN: 0895-4798,1095-7162
DOI: 10.1137/140967040