论文信息 - On the eigenvalues of the matrix pencilA+μB

On the eigenvalues of the matrix pencilA+μB

SummaryThe number of independent invariants ofn×n matricesA, B and their products on which the eigenvalues λ(μ) of the matrix pencilA+μB depend is determined by means of the theory of algebraic invariants and combinatorial analysis. Formulas are displayed for coefficients for the calculation of λ(μ) forn≤5.ZusammenfassungWir bestimmen die Anzahl der unabhängigen Invarianten dern×n MatrizenA, B und ihrer Produkte, von denen die Eigenwerte λ(μ) der MatrixbüschelA+μB abhängen, mittels der Theorie der algebraischen Invarianten und mittels kombinatorischer Analyse. Formeln für Koeffizienten zur Berechnung von λ(μ) werden angegeben fürn≤5.

L. E. Scriven | H. G. Othmer | H. Othmer | L. Scriven

[1] Tosio Kato. Perturbation theory for linear operators , 1966 .

[2] W. E. Roth,et al. On $k$-commutative matrices , 1936 .

[3] Further results in the theory of matrix polynomials , 1959 .

[4] H. W. Turnbull,et al. Lectures on Matrices , 1934 .

[5] L. E. Scriven,et al. A PHYSICOCHEMICAL BASIS FOR PATTERN AND RHYTHM , 1966 .

[6] L. E. Scriven,et al. Interactions of reaction and diffusion in open systems , 1969 .

[7] Alston S. Householder,et al. The Theory of Matrices in Numerical Analysis , 1964 .

[8] H. Weyl. The Classical Groups , 1939 .