An elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor

• 作者: Tianbo WANG Dinglin YANG Chen LI Diwei SHI
• 来源期刊: 应用数学和力学（英文版）
• 年，卷（期）: 2021,（5）
• 页码范围: 747-754
• 页数: 8页
• 分类号: O183.2
• 语种: 英文

摘要

Based on the Cayley-Hamilton theorem and fixed-point method,we provide an elementary proof for the representation theorem of analytic isotropic tensor functions of a second-order tensor in a three-dimensional(3D)inner-product space,which avoids introducing the generating function and Taylor series expansion.The proof is also extended to any finite-dimensional inner-product space.