TITLE: An upper estimate for $|\det(A+B)|$
QUESTION [7 upvotes]: If $A$ and $B$ are $n\times n$ matrices, then it easily follow from the definition of the determinant by sum over permutations, and from the Young inequality that
$$
|\det (A+B)|\leq C(n)(\Vert A\Vert^n+\Vert B\Vert^n),
$$
where $\Vert \cdot\Vert$ stands for the Hilbert-Schmidt norm of a matrix. I am looking for stronger/better/more elegant estimates (with references included) that would imply the above inequality.

REPLY [6 votes]: There is a paper by Chi-Kwong Li and Roy Mathias about lower and upper bounds for $|\det(A + B)|$ in terms of the singular values of $A$ and $B$. (The determinant of the sum of two matrices)