Principal minors, Part I: A method for computing all the principal minors of a matrix
نویسندگان
چکیده
منابع مشابه
Principal minors, Part I: A method for computing all the principal minors of a matrix
An order O(2n) algorithm for computing all the principal minors of an arbitrary n× n complex matrix is motivated and presented, offering an improvement by a factor of n3 over direct computation. The algorithm uses recursive Schur complementation and submatrix extraction, storing the answer in a binary order. An implementation of the algorithm in MATLAB is also given and practical considerations...
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The inverse problem of finding a matrix with prescribed principal minors is considered. A condition that implies a constructive algorithm for solving this problem will always succeed is presented. The algorithm is based on reconstructing matrices from their principal submatrices and Schur complements in a recursive manner. Consequences regarding the overdeterminancy of this inverse problem are ...
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The image of the principal minor map for n×n-matrices is shown to be closed. In the 19th century, Nansen and Muir studied the implicitization problem of finding all relations among principal minors when n = 4. We complete their partial results by constructing explicit polynomials of degree 12 that scheme-theoretically define this affine variety and also its projective closure in P15. The latter...
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The image of the principal minor map for n×n-matrices is shown to be closed. In the 19th century, Nansen and Muir studied the implicitization problem of finding all relations among principal minors when n = 4. We complete their partial results by constructing explicit polynomials of degree 12 that scheme-theoretically define this affine variety and also its projective closure in P15. The latter...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2006
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.04.008