scholarly journals On transformation partly preserving a nonsingular bilinear function

2005 ◽  
Vol 403 ◽  
pp. 273-284 ◽  
Author(s):  
Baodong Zheng ◽  
Yuqiu Sheng
Keyword(s):  
Bilinear Function

Groups Preserving a Class of Bilinear Functions

1985 ◽  
Vol 28 (3) ◽  
pp. 267-271
Author(s):  
W. H. Greub ◽  
J. Malzan ◽  
J. R. Vanstone
Keyword(s):  
Vector Space ◽  
Bilinear Function ◽  
Finite Dimensional ◽  
Euclidean Vector Space ◽  
Bilinear Functions

AbstractGiven a finite dimensional Euclidean vector space V, ( , ) and an involution τ of V, one can form the bilinear function ( , )τ defined by (x, y)τ = (τ(x), y), x,y ∊ V.Let O(τ) = {ϕ ∊ GL(V)|(ϕx, ϕy)τ = (x, y)τ}.If t is self-adjoint the structure of O(t) is well known. The purpose of this paper is to detemine the structure of O(t) in the general case. This structure is also determined in the complex and quaternionic case, as well as the case when the condition on t is replaced by τ2 = ∊ι, ∊ ∈ ℝ.

The Research of Covariance Matrix by the Nature of Bilinear Function

2013 ◽  
Vol 734-737 ◽  
pp. 3234-3237
Author(s):  
Yu Long Zhu ◽  
Tan Lin Tan
Keyword(s):  
Covariance Matrix ◽  
Product Space ◽  
Random Variable ◽  
Inner Product Space ◽  
Inner Product ◽  
Bilinear Function ◽  
Bilinear Functions

Covariance is a symmetric bilinear function on random variable inner product space,therefore we applied the methods and results of bilinear functions to the covariance matrix.

Sign in / Sign up

Export Citation Format

Share Document