Computing codimensions and generic canonical forms for generalized matrix products
نویسندگان
چکیده
منابع مشابه
Computing codimensions and generic canonical forms for generalized matrix products
A generalized matrix product can be formally written as A sp p A sp−1 p−1 · · ·A s2 2 A s1 1 , where si ∈ {−1,+1} and (A1, . . . , Ap) is a tuple of (possibly rectangular) matrices of suitable dimensions. The periodic eigenvalue problem related to such a product represents a nontrivial extension of generalized eigenvalue and singular value problems. While the classification of generalized matri...
متن کاملEla Computing Codimensions and Generic Canonical Forms for Generalized Matrix Products
A generalized matrix product can be formally written as A sp p A sp−1 p−1 · · ·A s2 2 A s1 1 , where si ∈ {−1,+1} and (A1, . . . , Ap) is a tuple of (possibly rectangular) matrices of suitable dimensions. The periodic eigenvalue problem related to such a product represents a nontrivial extension of generalized eigenvalue and singular value problems. While the classification of generalized matri...
متن کاملOn Apolarity and Generic Canonical Forms
The theory of apolarity was first developed by Clebsch, Lasker, Richw x mond, Sylvester, and Wakeford 10, 17, 20 . They were first interested in studying homogeneous polynomials of degree p and in q variables, and in expressing them as sums of pth powers of linear terms. The problem is to minimize the number of pth powers which are required in such a sum. For instance, a result due to Sylvester...
متن کاملNearly Optimal Algorithms for Canonical Matrix Forms
A Las Vegas type probabilistic algorithm is presented for nding the Frobenius canonical form of an n n matrix T over any eld K. The algorithm requires O~(MM(n)) = MM(n) (logn) O(1) operations in K, where O(MM(n)) operations in K are suucient to multiply two n n matrices over K. This nearly matches the lower bound of (MM(n)) operations in K for this problem, and improves on the O(n 4) operations...
متن کاملStructured canonical forms for products of (skew-) symmetric matrices and the matrix equation XAX=B
The contragredient transformation A 7→ PAP, B 7→ PBP of two matrices A,B effects simultaneous similarity transformations of the products AB and BA. This work provides structured canonical forms under this transformation for symmetric or skew-symmetric A,B. As an application, these forms are used to study the quadratic matrix equation XAX = B, where both A,B are skew-symmetric or symmetric matri...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Linear Algebra
سال: 2011
ISSN: 1081-3810
DOI: 10.13001/1081-3810.1440