On factor width and symmetric \(H\)-matrices
The factor width of a real symmetric matrix \(A\) is the smallest integer \(k\) such that there exists a real rectangular matrix \(V\) such that \(A=VV^T\) and each column of \(V\) contains at most \(k\) nonzero entries. It is proven that the set of symmetric real matrices with factor width at most two coincides with the class of generalized diagonally dominant matrices (the so-called \(H\)-matrices) with nonnegative diagonals. Some bounds of the factor width are also obtained.
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