Concept
Rank — where it appears
The number of independent directions a linear map's output can reach, which is the dimension of its image.
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.
What a map throws away
A linear map redraws the grid, and the determinant measures how much it stretches area. When that measurement comes out zero the map has flattened the plane onto a line — and the question worth asking is not how much was lost but how much survived, because the two always add to what there was.
Named alongside it
The objects these essays reach for when they reach for this one.
BasisDeterminantMatrixSingular matrixAreaDimensionImageKernelLinearityNullityOrientationProjection