7. If U¡¡ ‡ 0 are components of a tensor of the type (0, 2) and if the equation ƒU¡¡ + gU ji ³ = 0 holds ij w.r.t to a basis then prove that eitherf=g and Uij is skew-symmetric orf=-g and Uij is symmetric.
7. If U¡¡ ‡ 0 are components of a tensor of the type (0, 2) and if the equation ƒU¡¡ + gU ji ³ = 0 holds ij w.r.t to a basis then prove that eitherf=g and Uij is skew-symmetric orf=-g and Uij is symmetric.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:7. If Uj + 0 are components of a tensor of the type (0, 2) and if the equation fU¡j +gU ji
= 0 holds
w.r.t to a basis then prove that eitherf=g and Uj is skew-symmetric orf=-g and Uij is symmetric.
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