ELA, Volume 11, pp. 205-211, September 2004, abstract.
Determinant Preserving Transformations on Symmetric
Matrix Spaces
Chongguang Cao and Xiaomin Tang
Let S_n(F) be the vector space of n-by-n symmetric
matrices over a field F (with certain restrictions on
cardinality and characteristic). The transformations
phi on the space which satisfy one of the following
conditions:
1. det(A+ lambda B)= det(phi(A)+lambda phi(B))
for all A, B in S_n(F) and lambda in F;
2. phi is surjective and
det(A+ lambda B)=det(phi(A)+ lambda phi(B))
for all A, B and two specific lambda;
3. phi is additive and preserves determinant
are characterized.