1. ## isomorphism

Construct an isomorphism from the vector space of symmetric 2 x 2 matrices onto R^3

2. Originally Posted by lm6485
Construct an isomorphism from the vector space of symmetric 2 x 2 matrices onto R^3
Let $L:M_{22}\rightarrow\mathbb{R}^3$ s.t. $L\!\left(\begin{bmatrix}a & b \\ b & c\end{bmatrix}\right)=\begin{bmatrix}a \\ b \\ c\end{bmatrix}$ where $a,b,c\in\mathbb{R}$.

I leave it for you to show that this is indeed an isomorphism.