Basic Linear Algebra - Computer Graphics and Geometric Modeling - page 888

has the form

n

() =

ET aa d , (C.20)

for some unique constant d. This constant is of course the determinant of T and one
could make equation (C.20) the basis of a definition of the determinant. This can also
be used to define the determinant of a matrix. Advanced topics on algebra that discuss
multilinear maps often use this approach to determinants because, having developed
the machinery of tensors one then gets many of the properties of determinants for
almost “free.”