Relationships　between　entities　in　a　Knowledge　Base　(KB)　are　not　always　explicitly　expressed.　In　addition,　entities　may　implicitly　exist　within　explicit　ones.　These　phenomena　are　very　common　when　it　comes　to　large-scale　KBs.　Finding　implicit　relationships　in　a　KB　can　make　the　original　KB　more　meaningful　and　enhance　its　potential　in　real　world　applications.　In　this　paper,　we　focus　on　the　problem　of　finding　implicit-relationship　networks　in　large-scale　KBs.　Since　a　network　can　be　mathematically　expressed　as　a　matrix,　the　process　of　reasoning　for　implicit　relationship　finding　can　be　transformed　to　matrix　computation.　Considering　that　there　are　many　advantages　for　matrix　computation　instead　of　logic　based　and　graph　based　reasoning　(such　as　scalability　for　storage),　by　realizing　the　mathematical　nature　of　KBs,　we　use　matrix　transformation　and　computation　to　investigate　the　problem　of　implicit　relationship　finding.　We　give　several　illustrative　real　world　examples　using　large-scale　KBs　to　validate　this　framework.　In　addition,　we　also　investigate　the　potential　problems　of　scalability　on　matrix　storage,　as　well　as　the　cost　for　computation　and　time.　Based　on　the　proposed　approach　and　the　consideration　on　the　scalability　issue,　we　develop　the　MIRF　and　MIRF-L　algorithms　which　can　efficiently　process　this　kind　of　problem　if　the　rules　in　concrete　cases　can　be　clearly　expressed.　©　2011　IEEE.