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Basic tensor algebra

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December 13, 2020, 20:41	Basic tensor algebra	#1
TurbJet Senior Member Join Date: Oct 2017 Location: United States Posts: 233 Blog Entries: 1 Rep Power: 10	Greetings, I am confused by the following tensor operation: 1. tensor contraction $\pmb{A}:\pmb{A} = A_{ij}A_{ji}$ 2. tensor norm $\|\pmb{A}\| = (2A_{ij}A_{ij})^{1/2}$ What I am confused is if the algebra $A_{ij}A_{ji}$ is exactly the same as $A_{ij}A_{ij}$ . Am I right?

December 13, 2020, 21:02		#2
agd Senior Member Join Date: Jul 2009 Posts: 359 Rep Power: 19	Only if A is symmetric.

December 14, 2020, 05:25		#3
FMDenaro Senior Member Filippo Maria Denaro Join Date: Jul 2010 Posts: 6,947 Rep Power: 73	symmetry of the matrix is required, however being also aware of the fact that there are several types of matrix norm.

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