On orthogonal and special orthogonal invariants of a single matrix of small order
نویسندگان
چکیده
منابع مشابه
On the optimal correction of inconsistent matrix equations $AX = B$ and $XC = D$ with orthogonal constraint
This work focuses on the correction of both the coecient and the right hand side matrices of the inconsistent matrix equations $AX = B$ and $XC = D$ with orthogonal constraint. By optimal correction approach, a general representation of the orthogonal solution is obtained. This method is tested on two examples to show that the optimal correction is eective and highly accurate.
متن کاملAlmost Orthogonal Submatrices of an Orthogonal Matrix
Let t ≥ 1 and let n, M be natural numbers, n < M. Let A = (a i,j) be an n × M matrix whose rows are orthonormal. Suppose that for all j M n · n i=1 a 2 i,j 1/2 ≤ t.
متن کاملOn Orthogonal Matrix Polynomials
In this paper we deal with orthogonal matrix polynomials. First of all, we establish some basic notations and results we need later. A matrix polynomial P is a matrix whose entries are polynomials, or, equivalently, a combination P(t) = A 0 +A 1 t+ +A n t n , where A 0 ; ; A n are numerical matrices (the size of all the matrices which appear in this paper is N N). A positive deenite matrix of m...
متن کاملOn orthogonal invariants in characteristic 2
Working over an algebraically closed base field k of characteristic 2, the ring of invariants R is studied, where G is the orthogonal group O(n) or the special orthogonal group SO(n), acting naturally on the coordinate ring R of the m-fold direct sum k⊕ · · · ⊕ k of the standard vector representation. It is proved for O(2), O(3) = SO(3), SO(4), and O(4), that there exists an m-linear invariant ...
متن کاملMod 2 Indecomposable Orthogonal Invariants
Over an algebraically closed base field k of characteristic 2, the ring R of invariants is studied, G being the orthogonal group O(n) or the special orthogonal group SO(n) and acting naturally on the coordinate ring R of the m–fold direct sum k ⊕ · · · ⊕ k of the standard vector representation. It is proved for O(n) (n ≥ 2) and for SO(n) (n ≥ 3) that there exist m–linear invariants with m arbit...
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: Linear and Multilinear Algebra
سال: 2009
ISSN: 0308-1087,1563-5139
DOI: 10.1080/03081080701669333