For n by k matrices with k >= 4, n >= k+2 and n+k odd, linear preservers of the Cullis determinant are sums of two-sided multiplications and maps sending everything to equal-row matrices.
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Linear maps preserving the Cullis' determinant. II
For n by k matrices with k >= 4, n >= k+2 and n+k odd, linear preservers of the Cullis determinant are sums of two-sided multiplications and maps sending everything to equal-row matrices.