Suppose we have following speical block skew symmetric matrix $$ X = \begin{bmatrix} 0 & X_3 & -X_2\\ -X_3& 0& X_1\\ X_2 &-X_1 &0 \end{bmatrix} $$ where $X_1,X_2,X_3\in R^{n \times n}$ and not invertible,can we determine the rank of X via the combination of $X_1$,$X_2$ and $X_3$ like ${\rm rank}(X)$=${\rm rank}(X_1-X_3)$+${\rm rank}(X_2X_3)$?It seems difficuty to obtained $X$ by elementary transformation
2026-03-27 04:38:32.1774586312
The rank of block skew symmetric matrix
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