Hyperbolic Systems of Partial Differential Equations

Similarly, the vector-column r = [r\,..., rn]T is called a right eigenvector of a matrix A if

(1.1.4) Owing to Eqs. (1.1.3)—(1.1.4), the eigenvalue A of the matrix A is the root of the

characteristic equation (1.1.5)

where / = diag[l,..., 1] is the n x n identity matrix. Suppose all the eigenvalues À of the matrix A are real. Let us enumerate them in

increasing order, that is, (1.1.6)

then both the right and left eigenvectors corresponding to all eigenvalues form a basis in the Euclidean space En(u).