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PSYCHO15rus [73]
4 years ago
5

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

Mathematics
1 answer:
WARRIOR [948]4 years ago
6 0
A matrix \mathbf X is symmetric if \mathbf X=\mathbf X^\top. We have

(\mathbf B+\mathbf B^\top)^\top=\mathbf B^\top+(\mathbf B^\top)^\top=\mathbf B^\top+\mathbf B=\mathbf B+\mathbf B^\top

and so \mathbf B+\mathbf B^\top is indeed symmetric.
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