Cracovian

In astronomical and geodetic calculations, Cracovians are a clerical convenience introduced in the 1930s by Tadeusz Banachiewicz for solving systems of linear equations by hand. Such systems can be written as Ax = b in matrix notation where x and b are column vectors and the evaluation of b requires the multiplication of the rows of A by the vector x. Since (AB)T = BTAT, the products (A ∧ B) ∧ C and A ∧ (B ∧ C) will generally be different; thus, Cracovian multiplication is non-associative. Cracovians are an example of a quasigroup.

Cracovian

In astronomical and geodetic calculations, Cracovians are a clerical convenience introduced in the 1930s by Tadeusz Banachiewicz for solving systems of linear equations by hand. Such systems can be written as Ax = b in matrix notation where x and b are column vectors and the evaluation of b requires the multiplication of the rows of A by the vector x. Since (AB)T = BTAT, the products (A ∧ B) ∧ C and A ∧ (B ∧ C) will generally be different; thus, Cracovian multiplication is non-associative. Cracovians are an example of a quasigroup.