Gradient
Named by 3 essays across 2 fields — each of them below, with the objects they name alongside it.
A line under every point
The chord above the curve is one definition of convexity. There is a second — a line under the curve at every point, staying under everywhere — and it is the one that turns a statement about a derivative at a point into a statement about the whole function.
Where the guarantee stops
Convexity converts every downhill method into a correct one, and its absence removes the guarantee entirely rather than degrading it. What is left is a collection of partial answers, and knowing which of them apply to a given problem is most of what non-convex optimisation is.
Moving a map across a product
The transpose looks like a fact about a matrix: reflect its entries in the diagonal. It is a fact about the inner product. Measure lengths and angles differently and the map that slides to the other side of the product is a different matrix, and a matrix that was symmetric stops being so.
Named alongside it
The objects these essays reach for when they reach for this one.
ConvexityLocal minimumOptimisationAdjointComplexityCounterexampleDerivativeEigenvectorInequalityInner productLeast squaresMarkov chain