Prove that the set of $n\times n$ symmetric matrices is a subspace of $M_{n\times n}(R)$?

Question

Let H be the set of all symmetric $n\times n$ matrices:

$H = \{A ∈ M_{n\times n}(R) | A^T = A\}$.

Prove that H is a subspace of $M_{n\times n}(R)$.

This is even a more general duplicate, but the one I linked is more useful. Please search for your question before posting it, in the future. — rschwieb, Dec 14 '17 at 14:29

score 4 · Accepted Answer · answered Dec 14 '17 at 14:14

4

You have to show: if $A,B \in H$ and $\alpha \in \mathbb R$, then

$A+B \in H$ amd $ \alpha A \in H$.

answered Dec 14 '17 at 14:14

Fred

1 Answers1