First, a small note: an m-by-n or m x n matrix has m rows and n columns. The eigenvalues λ of a matrix A are scalars such that Ax = λx for some nonzero x vector. The entries aij of a matrix A are...
The eigen values of a matirx are the values L such that Ax = Lx
where A is a matrix, x is a vector, and L is a constant.
The vector x is known as the eigenvector.
One way of dividing animals is into herbivores, carnivores, and omnivores. The division is rather fuzzy (cats sometimes eat grass), and incomplete (there is such a thing as a detritivore). But it is...