A Frobenius matrix or atomic triangular matrix is a square matrix with the following properties:

  • All entries on the main diagonal are ones
  • The matrix only has one column where some entries below the main diagonal can be non-zero
  • Al other entries outside the main diagonal equal zero

Example:

Inverse of a Frobenius matrix

If is a Frobenius matrix, then its inverse is also a Frobenius matrix, where the corersponding nonzero entries outside the main diagonal have opposite signs.