A type (0,4) tensor Tabed satisfies Tabcd A® µ°A°µ¢ = 0 for all con- travariant vectors X and uº. Show that its components satisfy Tabcd + Tcbad + Tadcb + Tedab :0.

Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
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Chapter1: Vectors
Section1.1: The Geometry And Algebra Of Vectors
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A type (0,4) tensor Tabcd satisfies TabcddªµX°µd = 0 for all con-
travariant vectors Xª and uº. Show that its components satisfy
Tabcd + Tebad+ Tadcb + Tcdab =
0.
Transcribed Image Text:A type (0,4) tensor Tabcd satisfies TabcddªµX°µd = 0 for all con- travariant vectors Xª and uº. Show that its components satisfy Tabcd + Tebad+ Tadcb + Tcdab = 0.
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