交错阵的线性保持问题

【作者】 李强；

【导师】 曹重光；

【作者基本信息】 黑龙江大学 ， 基础数学， 2004， 硕士

【摘要】 设F是域，R为实数域，本文主要研究交错阵的两个线性保持问题。当char F≠2时，交错阵就是反对称矩阵。令SK_n(F)为F上所有n×n反对称矩阵构成的空间，M_n(F)为F上所有n×n全矩阵构成的空间，T_n(F)为F上所有n×n上三角矩阵构成的空间。 一方面，在文献[43]中刻画了从M_n(F)到M_n(F)与从T_n(F)到T_n(F)的行列式保持映射，本文则刻画了SK_n(R)到SK_n(R)的行列式保持映射的形式；另一方面，在文献[7]中刻画了当F是特征不为2的无限域，n为偶数时，SK_n(F)到SK_n(F)的保伴随的线性映射，本文则刻画了当char F≠2，n为偶数时，SK_n(F)到SK_n(F)的保伴随的线性映射的形式。更多还原

【Abstract】 Let F be a field, R be a real field, this paper mainly studys two linear preserver problems on alternate matrices. When charF 2, alternate matrices is skew-symmetric matrices. Let SKn(F) be the vector space of n x n skew-symmetric matrices over the field F, Mn(F) be the vector space of n x n matrices over the field .F, Tn(F) be the vector space of n x n upper triangular matrices over the field F.On one hand,the mapping preserving determinant is characterised from Mn(F) to Mn(F) and from Tn(F) to Tn(F) in reference [43], however,in this paper, we characterise the forms of mapping preserving determinant from SKn(R) to SKn(K); on the other hand.when F is an infinite field with charF ^ 2 and n is a positive even,the linear mapping preserving adjugate from SKn(F) to SKn(F) is characterised in reference [7],however,in this paper,when char F ^ 2, n is a positive even,we characterise the forms of linear mapping preserving adjugate from SKn(F) to SKn(F).更多还原