the dim(u)=6 is understandable but dim(S)=6.....I don't get it. Can some body tell me the basis for symmetric 3X3 matrices

Question

anonymous · Answer

dimension just means the number of vectors in the basis. one basis i can think of is
$$\left[\begin{matrix}1 & 0 & 0 \0 & 0 & 0 \0 & 0 & 0 \end{matrix}\right],\left[\begin{matrix}0 & 0 & 0 \0 & 1 & 0 \0 & 0 & 0 \end{matrix}\right],\left[\begin{matrix}0 & 0 & 0 \0 & 0 & 0 \0 & 0 & 1 \end{matrix}\right],\left[\begin{matrix}0 & 1 & 0 \1 & 0 & 0 \0 & 0 & 0 \end{matrix}\right],\left[\begin{matrix}0 & 0 & 1 \0 & 1 & 0 \1 & 0 & 0 \end{matrix}\right],\left[\begin{matrix}0 & 0 & 0 \0 & 0 & 1 \0 & 1 & 0 \end{matrix}\right]$$