Concept
Determinant
The factor by which a linear map multiplies area or volume, together with the sign saying whether it turns the space over as well.
Named by 2 essays across one field — each of them below, with the objects they name alongside it.
A matrix is a picture of what happens to the grid
Four numbers in a box is not an object anyone has intuitions about. The same four numbers, shown as an instruction for redrawing the plane, are.
The directions a map leaves alone
Almost every arrow comes out of a transformation pointing somewhere else. A few come out pointing exactly where they went in, only longer or shorter. Those few decide nearly everything the map does.
Named alongside it
The objects these essays reach for when they reach for this one.
BasisMatrixShearAreaCharacteristic polynomialDiagonalisationEigenvalueEigenvectorInvariant directionOrientationOrthogonalityRank