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02-10-2017
Mathematics

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Prove that if b is a square matrix then b+b^t is symmetric

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LammettHash LammettHash

02-10-2017

A matrix [tex]\mathbf X[/tex] is symmetric if [tex]\mathbf X=\mathbf X^\top[/tex]. We have

[tex](\mathbf B+\mathbf B^\top)^\top=\mathbf B^\top+(\mathbf B^\top)^\top=\mathbf B^\top+\mathbf B=\mathbf B+\mathbf B^\top[/tex]

and so [tex]\mathbf B+\mathbf B^\top[/tex] is indeed symmetric.

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