منابع مشابه
Exterior Powers
Let R be a commutative ring. Unless indicated otherwise, all modules are R-modules and all tensor products are taken over R, so we abbreviate ⊗R to ⊗. A bilinear function out of M1 × M2 turns into a linear function out of the tensor product M1 ⊗ M2. In a similar way, a multilinear function out of M1 × · · · ×Mk turns into a linear function out of the k-fold tensor product M1 ⊗ · · · ⊗Mk. We wil...
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A signed graph is a graph whose edges are given ±1 weights. In such a graph, the sign of a cycle is the product of the signs of its edges. A signed graph is called balanced if its adjacency matrix is similar to the adjacency matrix of an unsigned graph via conjugation by a diagonal ±1 matrix. For a signed graph Σ on n vertices, its exterior kth power, where k = 1, . . . , n−1, is a graph ∧k Σ w...
متن کاملMinors of Symmetric and Exterior Powers
We describe some of the determinantal ideals attached to symmetric, exterior and tensor powers of a matrix. The methods employed use elements of Zariski's theory of complete ideals and of representation theory. Let R be a commutative ring. The determinantal ideals attached to matrices with entries in R play ubiquitous roles in the study of the syzygies of R{modules. In this note, we describe so...
متن کاملExterior Powers of Symmetric Bilinear Forms
We study exterior powers of classes of symmetric bilinear forms in the WittGrothendieck ring of a field of characteristic not equal to 2, and derive their basic properties. The exterior powers are used to obtain annihilating polynomials for quadratic forms in the Witt ring. 1991 AMS Subject Classification: 11E04, 11E81
متن کاملThe variety of exterior powers of linear maps
Let V and W be vector spaces of dimension m and n resp. We investigate the Zariski closure Xt of the image Yt of the map HomK(V,W ) → HomK( ∧t V, ∧t W ), φ 7→ ∧t φ . In the case t = min(m,n), Yt = Xt is the cone over a Grassmannian, but for 1 < t < min(m,n) one has Xt 6= Yt . We analyze the G = GL(V )×GL(W )-orbits in Xt via the G-stable prime ideals in O(Xt). It turns out that they are classif...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 1977
ISSN: 0024-3795
DOI: 10.1016/0024-3795(77)90026-x