# Difference between \langle and <

Is there any difference between \langle S \rangle and \left< S \right>? Or is \langle just an alias for < that by default works on one line without having to use \left?

• Unrelated to TeX, but in Unicode: <> are U+003C/U+003E LESS-THAN SIGN/GREATER-THAN SIGN, while ⟨⟩ are U+27E8(/U+27E9) MATHEMATICAL LEFT(/RIGHT) ANGLE BRACKET. Also punctuation: ‹› U+2039(/U+203A) SINGLE LEFT/(RIGHT)-POINTING ANGLE QUOTATION MARK. Then as wide characters (CJK), there are 〈〉 U+3008/U+3009 LEFT/RIGHT ANGLE BRACKET; and (deprecated) 〈〉 (deprecated) U+2329/U+232A LEFT/RIGHT-POINTING ANGLE BRACKET (both deprecated). There are also ornaments like ❬❭ (U+276C and U+276D), ❮❯ (U+276E and U+276F), ❰❱ (U+2770 and U+2771). Hopefully when I next search for langle/rangle I can find this :) – ShreevatsaR Dec 17 '19 at 16:13

<...> just puts in the font's normal '<' and '>' characters as binary relations. As Mark S. Everitt said, you almost never want this.

\langle ...\rangle inserts a completely different set of characters which are narrower and taller than '<' and '>'. It also puts them in as delimiters, which means they get special spacing and have a slightly different shape in \scriptstyle (used for, e.g., superscripts).

\left<...\right> is an alias for \left\langle ...\right\rangle. These do not do the same thing as \langle ...\rangle! The differences are described in this answer, but the main things are that \left<...\right> scales to its contents and adds extra space sometimes.

EDIT: Another important difference is that \langle and \rangle (or \bigl< and \bigr>) may be used alone, since they're just delimiters. \left must always be followed by \right, which is why \right. (the blank delimiter) exists. Also, in case it wasn't clear, \langle does not really care what's in the rest of the equation, since it doesn't scale to contents.

Don't use < or > like this. They are relations, whereas \langle and \rangle are delimiters. If you find typing them laborious, wrap them in macros (I do this with new commands like \ket{...} and \bra{...}.

Without \left and \right prepended to both, you get these:

With \left and \right on both the output is the same (both resize automatically) as you note in the question. I strongly advise you to use \langle and \rangle (with or without \left and \right) because every time I see a Dirac ket like this

my eyes bleed. If you always use \langle and \rangle then you can treat them just like other types of variable sized delimiter and get no ugly surprises. I know that this doesn't quite answer your question, but there may be people looking at this question who didn't realise you could use > like this and I want to nip that in the bud right now!

• I kinda knew that; |A> makes me twitch as well. I just wanted to know if there was any difference in the TeX or if langle was an alias. But thanks for getting the message across. :) – Manishearth Mar 7 '12 at 11:16
• Yeah, sorry about that. I saw > and had a bit of an allergic reaction! I am aware that the question was really one of what's going on behind the scenes though. :) – qubyte Mar 7 '12 at 11:57
• +1 for bleeding eyes with poor quantum mechanics notation – cm2 Mar 7 '12 at 17:25
• My brain bleeds whenever I see bra ket notation. I just never got my head around it. – Seamus Mar 7 '12 at 17:38
• @Seamus: It avoids a lot of integration, and that makes my brain bleed more. Lesser of two evils. – qubyte Mar 7 '12 at 17:40