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...Matrixcalculus notesonthederivativeofatrace johannestraa this write up elucidates the rules of matrix calculus for expressions involving trace a function x f tr g wewouldliketotakethederivativeof withrespecttox one strategy is to expression as scalar using index notation take derivative and re in form an easier way reduce problem or moresmallerproblemswheretheresultsforsimplerderivativescanbeapplied it sbrute forcevsbottom valuedderivative thederivativeofascalar withrespecttoamatrixx rm n canbewrittenas xn xm xmn so result same size matrixandindexnotation useful be able convert between example theproductabhaselements ik xaijbjk j andthematrixproductabct haselements t xx abc il aij bc jl k bjkclk aijbjkclk first order derivatives considerthisexample axb wecanwritethisusingindexnotationas xxa xb b xxxa ii i ji jk ki takingthederivativewithrespectto xjk weget xa ba kj has we know that indices rows columnsmustbe andk respectively means have transpose above towritethederivativeinmatrixforma...