Exercise 1.3.5

Prove that $A + A^{t}$ is symmetric for any square matrix $A$ .

Answers

Proof. Using previous exercises, we obtain

{(A + A^{t})}^{t} = A^{t} + {(A^{t})}^{t} = A^{t} + A .

In other words, it’s symmetric. □

jephianlin

2011-06-27 00:00