What it means
An upside-down triangle for the vector of partial derivatives. Alone, ∇f is the gradient: the direction of steepest increase of f. With a dot, ∇ · F is the divergence of a field; with a cross, ∇ × F is its curl; squared, ∇² is the Laplacian.
Read aloud in real formulas
θ ← θ − η ∇L(θ)
Aethel says
theta is updated to theta minus eta times the gradient of L of theta
a step against the gradient of the loss
∇ · E = ρ / ε₀
Aethel says
the divergence of E equals rho over epsilon naught
the divergence of the electric field
∇ × E = −∂B/∂t
Aethel says
the curl of E equals negative the partial derivative of B with respect to t
the curl of the electric field
Typing it
- LaTeX
- \nabla
- Unicode
- U+2207
Formulas that use it
Questions
How do you say ∇ out loud?
It is usually read “del”, and also “nabla” or “the gradient of”.
What does ∇ mean in maths?
An upside-down triangle for the vector of partial derivatives. Alone, ∇f is the gradient: the direction of steepest increase of f. With a dot, ∇ · F is the divergence of a field; with a cross, ∇ × F is its curl; squared, ∇² is the Laplacian.
How do you type ∇?
In LaTeX, write \nabla. Its Unicode code point is U+2207.
What is ∇ often confused with?
It is easy to mistake for the capital Greek Δ, which points the other way and means a change.