In mathematics, the spectrum of a (finite-dimensional) matrix is the set of its eigenvalues. This notion can be extended to the spectrum of an operator in the infinite-dimensional case.
The determinant equals the product of the eigenvalues. Similarly, the trace

Trace (linear algebra)

In linear algebra, the trace of an n-by-n square matrix A is defined to be the sum of the elements on the main diagonal of A, i.e.,...

 equals the sum of the eigenvalues.
From this point of view, we can define the Pseudo-determinant

Pseudo-determinant

In linear algebra and statistics, the pseudo-determinant is the product of all non-zero eigenvalues of a square matrix. It coincides with the regular determinant when the matrix is non-singular.- Definition :...

 for a singular matrix to be the product of all the nonzero eigenvalues (the density of Multivariate normal distribution will need this quantity).