Chapter 4: Traces, Determinants and Hyperdeterminants

A function on n × n matrices det : ℂ^n×n → ℂ is called a determinant function if and only if it satisfies the following conditions:

• det is linear in each row if the other rows of the matrix are held fixed.

• If the n × n matrix A has two identical rows then det(A) = 0.

• If I_n is the n × n identity matrix, then det(I_n) = 1.