Adjoint
Named by 2 essays across 2 fields — each of them below, with the objects they name alongside it.
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.
A slope without a subtraction
The definition of a slope subtracts two nearly equal numbers and divides by a tiny one, and a computer that follows it loses half its digits however carefully the step is chosen. Two pieces of arithmetic avoid the subtraction altogether. Step sideways into the complex numbers by 10⁻²⁰⁰ and read off the imaginary part; or calculate with numbers a + bε in which ε² = 0, and the slope rides along exactly. Run backwards, the second gives all thousand slopes of a function of a thousand variables for under five times the cost of the function.
Named alongside it
The objects these essays reach for when they reach for this one.
GradientChain ruleComplex numbersDerivativeDifference quotientEigenvectorFloating-pointInner productLeast squaresMarkov chainOrthogonalityPositive definite