Starting　from　the　local　structures　to　study　hierarchical　trees　is　a　common　research　method.　However,　the　cumbersome　analysis　and　description　make　the　naive　method　challenging　to　adapt　to　the　increasingly　complex　hierarchical　tree　problems.　To　improve　the　efficiency　of　hierarchical　tree　research,　we　propose　an　embeddable　matrix　representation　for　hierarchical　trees,　called　Generation　Matrix.　It　can　transform　the　abstract　hierarchical　tree　into　a　concrete　matrix　representation　and　then　take　the　hierarchical　tree　as　a　whole　to　study,　dramatically　reducing　the　research　complexity.　Mathematical　analysis　shows　that　Generation　Matrix　can　simulate　various　recursive　algorithms　without　accessing　local　structures　and　provides　a　variety　of　interpretable　matrix　operations　to　support　the　research　of　hierarchical　trees.　Applying　Generation　Matrix　to　differential　privacy　hierarchical　tree　release,　we　propose　a　Generation　Matrix-based　optimally　consistent　release　algorithm　(GMC).　It　provides　an　exceptionally　concise　process　description　so　that　we　can　describe　its　core　steps　as　a　simple　matrix　expression　rather　than　multiple　complicated　recursive　processes　like　existing　algorithms.　Our　experiments　show　that　GMC　takes　only　a　few　seconds　to　complete　a　release　for　large-scale　datasets　with　more　than　10　million　nodes.　The　calculation　efficiency　is　increased　by　up　to　100　times　compared　with　the　state-of-the-art　schemes.　©　2023　Elsevier　B.V.