Concept
Singular matrix
A matrix that collapses space onto something smaller, so that it cannot be undone and its determinant is zero.
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 number that says how much room is left
A linear map takes the unit square to a parallelogram. The area of that parallelogram is one number, it is computable from the four entries of the matrix, and almost everything the determinant is used for is a restatement of that sentence.
Named alongside it
The objects these essays reach for when they reach for this one.
AreaBasisDeterminantMatrixOrientationShearEigenvalueInvariant directionRankScaling