NapkinCalc

Linear Algebra — Matrices

Matrices & the determinant

Enter a matrix with rows separated by ;. Its determinant is the single most informative number about it: the factor by which the machine scales area. Determinant zero means the machine flattens space — and flattening cannot be undone.

M:=[2,1;1,3]M := [2, 1; 1, 3] = [[2,1],[1,3]][[2, 1], [1, 3]] a 2×2 matrix
dM=det(M)d_{M} = \mathrm{det}\left(M\right) = 55 areas come out 5× bigger
Mflat:=[2,4;1,2]M_{flat} := [2, 4; 1, 2] = [[2,4],[1,2]][[2, 4], [1, 2]] second row is half the first…
dflat=det(Mflat)d_{flat} = \mathrm{det}\left(M_{flat}\right) = 00 …so it flattens: det = 0, no inverse exists