Trace identities from identities for determinants

Stephen Humphries, Christian Krattenthaler

We present new identities for determinants of matrices $(A_{i,j})$ with entries $A_{i,j}$ equal to $a_{i,j}$ or $a_{i,0}{a}_{0,j}-a_{i,j}$, where the $a_{i,j}$'s are indeterminates.…