Matrix multiplication Definition 7.1.3(Matrix multiplication) Let A=(ay)mxs and B=(bi)sxn.Then AB=(cy)mxn.where cg=a1b1y+…十asbg=k=1 aikbij,(=1,…,m;j=1,…,n） Special Cases IAmxnOnxs=Omx Osxm4mx=0xxn 24m×:= m行= Proof:Let C=AE.then we have Tongji University】 5/14Matrix multiplication . Definition 7.1.3 (Matrix multiplication) . . Let A = (aij)m×s and B = (bij)s×n . Then AB = (cij)m×n, where cij = ai1b1j + · · · + aisbsj = ∑s k=1 aikbkj , (i = 1, · · · , m; j = 1, · · · , n) . Special Cases . . 1. Am×nOn×s = Om×s , Os×mAm×n = Os×n 2. Am×nEn = A; EmAm×n = A. Proof: Let C = AE, then we have: cij = ∑n k=1 aikδkj = aijδjj = aij. (Tongji University) Linear Algebra 5 / 14