A note on an unusual type of generalized polar decomposition

Inspired by the paper of Faßbender and Ikramov [H. Faßbender, Kh.D. Ikramov, A note on an unusual type of polar decomposition, Linear Algebra Appl. 429 (2008) 42–49], in this note we introduce an unusual type of generalized polar decomposition for a rectangular matrix A of the form A=GE, where G is a complex symmetric matrix and E is a partial isometric matrix. Following the pattern used in the paper mentioned above, we call this decomposition a symmetric-partial-isometric generalized polar decomposition or an SPIGPD for short. Some properties of this decomposition are presented and results of SPIGPD related to conjugate-normal matrices are also obtained.