Symbols · Notation and constants
⟨x, y⟩ Inner product (angle brackets)
Say it: “the inner product of x and y”
What it means
Angle brackets around two vectors give their inner product, a generalised dot product. In quantum mechanics, bras and kets such as ⟨ψ| and |ψ⟩ build on the same idea; in physics ⟨x⟩ can also mean an average.
Read aloud in real formulas
⟨x, y⟩ = 0
Aethel says
the inner product of x and y equals 0
x and y are orthogonal
Typing it
- LaTeX
- \langle x, y \rangle
- Unicode
- U+27E8, U+27E9
Questions
How do you say ⟨ , ⟩ out loud?
It is usually read “the inner product of x and y”.
What does ⟨ , ⟩ mean in maths?
Angle brackets around two vectors give their inner product, a generalised dot product. In quantum mechanics, bras and kets such as ⟨ψ| and |ψ⟩ build on the same idea; in physics ⟨x⟩ can also mean an average.
How do you type ⟨ , ⟩?
In LaTeX, write \langle x, y \rangle. Its Unicode code point is U+27E8, U+27E9.