TITLE: Is there a name for a block-diagonal matrix with blocks of the form $\begin{pmatrix} 0 & a \\ -a & 0 \end{pmatrix}$?
QUESTION [6 upvotes]: Is there a name for a real square matrix of the form
$$\begin{pmatrix}
0 & a_1 \\ -a_1 & 0 \\
& & 0 & a_2 \\ & & -a_2 & 0 \\
& & & & \ddots \\
& & & & & 0 & a_k \\
& & & & & -a_k & 0
\end{pmatrix}$$
optionally with one or more additional rows/columns of 0?
For example, analogous to the fact that a real symmetric matrix is orthogonally equivalent to a real diagonal matrix, we can show that a real skew-symmetric matrix is orthogonally equivalent to a matrix of the form above.

REPLY [9 votes]: The above is a quasi-diagonal skew-symmetric matrix. Obviously, I don't need to explain the skew-symmetric part.
The term "quasi-diagonal" means "block-diagonal with the diagonal blocks of order at most $2$". They are studied, for example, here. The name is chosen with respect to quasi-triangular matrices which are often used in real Schur and similar decompositions (see here).
The term itself is mentioned here.