关于非奇异线性变换依赖于方向的分解

A Decomposition Depended on Directions for Non Singular Linear Transformation

本文给出了ｎ（ｎ≥３）维欧氏空间Ｅｎ上非奇异线性变换Ｆ依赖于任意给定的Ｐ（１≤Ｐ≤ｎ—２）个正交方向的分解，进而证明了Ｆ依赖于上述Ｐ个正交方向的ｎ（ｑ＝ｎ—Ｐ）个准主向的存在．作为上述结果的应用，我们推导出了处于均匀变形的物体中任意平面内至少存在两个互相正交的应变主方向，以及该物体内应变能密度在上述线性变换的任意一个准主基下可表为５个实数的函数．

In this paper, we give a decomposition depending on p(1≤p≤n-2) or thonormal directions assigned for non singular linear transformation F on a n-dimens ion (n≥3) Euclidean space En and then prove that there exist q(q= n-p)quasiprincipal directions for F depending on the preceding p orthonormal directions.As applicance of the preceding result, we derive that there exist at least two orthonormal principal directions of strain in arbitrary plane of body which is in homogeneous deformation, and strain energy density is function of 5 real numbers under arbitrary quasi-principal base for the preceding non singular linear transformation.