diff --git a/dotfiles/neovim/ftplugin/tex.lua b/dotfiles/neovim/ftplugin/tex.lua
index 08daa65..6415712 100644
--- a/dotfiles/neovim/ftplugin/tex.lua
+++ b/dotfiles/neovim/ftplugin/tex.lua
@@ -85,6 +85,8 @@ local abbreviations = {
   { "card", "\\#" },
   { "div", "\\|" },
   { "ndiv", "\\not\\|\\:" },
+  { "perp", "\\perp" },
+  { "iprod", "\\iprod" }, -- custom inner product command
 
   -- words
   { "rref", "reduced row echalon form" },
diff --git a/dotfiles/vscode-snippets/snippets/latex/core.json b/dotfiles/vscode-snippets/snippets/latex/core.json
index b609911..d36d105 100644
--- a/dotfiles/vscode-snippets/snippets/latex/core.json
+++ b/dotfiles/vscode-snippets/snippets/latex/core.json
@@ -206,7 +206,7 @@
   "Aligned display math": {
     "prefix": "maligned",
     "description": "Create an aligned display math environment",
-    "body": ["\\begin{align}", "\t$0", "\\end{align}"]
+    "body": ["\\begin{align*}", "\t$0", "\\end{align*}"]
   },
   "System of equations": {
     "prefix": "eqsystem",