I'm reading the book "Int. to Applied Nonlinear Dynamical Systems and Chaos By Stephen Wiggins" and this book find the following affirmation.
In the four-dimensional space of $2 \times 2$ real matrices the matrices $$\left(\begin{matrix}0&-\omega\\\omega&0 \end{matrix}\right), \hspace{2mm}(\star) $$ and $$\left(\begin{matrix}0&1\\0&0 \end{matrix}\right)$$ lie on surfaces of codimension 2.
But I don't know how prove this affirmation. In first stage I try to identify $M_{2\times2 }\equiv \mathbb{R}^{4}$ and the set of matrices in the form $\star$ with $\mathbb{R}^{2}$ and so justify why at least in this case we have codimension 2, but if it work in the other case this not work. It was my attempt but don't work. How can I prove this affirmation?
Thanks in advance.