Spectral cones in Euclidean Jordan algebras
Spectral cones in Euclidean Jordan algebras
复制标题
欧几里得约旦代数中的谱锥
DOI：
10.1016/j.laa.2016.08.004
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发表时间：
2016
影响因子：
1.1
通讯作者：
M. Gowda
中科院分区：
文献类型：
--
作者：
Juyoung Jeong;M. Gowda
秩为n的欧氏若当代数V中的谱锥的形式为K= λ− 1（Q），其中Q是Rn中的置换不变凸锥，λ：V→ Rn是特征值映射（将x取为λ（x），即x的特征值向量，其中元素按降序写入）。本文描述了谱锥的一些性质。例如，我们证明了谱锥在V的自同构下是不变的，当V是简单的或带有正则内积时，谱锥的对偶是谱锥，并刻画了谱锥的尖性/实性。我们还证明了对于V中的任何谱锥K，dim（K）∈{0，1，m− 1，m}，其中dim（K）表示K的维数，m是V的维数。
A spectral cone in a Euclidean Jordan algebra V of rank n is of the form K= λ− 1 (Q), where Q is a permutation invariant convex cone in R n and λ: V→ R n is the eigenvalue map (which takes x to λ (x), the vector of eigenvalues of x with entries written in the decreasing order). In this paper, we describe some properties of spectral cones. We show, for example, that spectral cones are invariant under automorphisms of V, that the dual of a spectral cone is a spectral cone when V is simple or carries the canonical inner product, and characterize the pointedness/solidness of a spectral cone. We also show that for any spectral cone K in V, dim(K)∈{0, 1, m− 1, m}, where dim(K) denotes the dimension of K and m is the dimension of V.