This expository paper establishes the canonical forms under congruence for pairs of complex or real symmetric or skew matrices. The treatment is in the spirit of the well-known book of Gantmacher on matrix theory, and may be regarded as a supplement to Gantmacher's chapters on pencils of matrices. © 1991.
Thompson, R. C. (1991). Pencils of complex and real symmetric and skew matrices. Linear Algebra and Its Applications, 147(C), 323–371. https://doi.org/10.1016/0024-3795(91)90238-R