[4][5][6] From this point of view, we can define the pseudo-determinant for a singular matrix to be the product of its nonzero eigenvalues (the density of multivariate normal distribution will need this quantity).
In many applications, such as PageRank, one is interested in the dominant eigenvalue, i.e. that which is largest in absolute value.
In other applications, the smallest eigenvalue is important, but in general, the whole spectrum provides valuable information about a matrix.
Define the linear map T : V → V pointwise by Tx = Mx, where on the right-hand side x is interpreted as a column vector and M acts on x by matrix multiplication.
The spectral radius of a square matrix is the largest absolute value of its eigenvalues.