In　his　paper,　the　matrix　multiplication　theory　is　utilized　to　obtain　Loeffler＇s　DCT　algorithm　and　Feig＇s　DCT　algorithm.　In　addition,　the　Feig＇s　algorithm　is　extended　to　other　three　forms.　Utilizing　matrix　decomposition　representation,　the　links　and　differences　between　the　two　algorithms　are　revealed.　This　decomposition　representation　helps　understanding　and　further　improving　the　algorithms　using　matrix　theory.　©　2005　IEEE.