The canonical structure of a pencil of degenerate matrix functions
The author studies global properties of a pencil of identically degenerate matrix functions with a compact domain of definition. The matrix functions are assumed to have a constant rank and all roots of the characteristic equation of the matrix pencil are assumed to have a constant multiplicity at each point in the domain of definition. He obtains sufficient conditions for the smooth orthogonal similarity of the matrix functions to the upper triangular form and sufficient conditions for the smooth equivalence of the pencil of matrix functions to its canonical form. He also illustrates the obtained results with simple examples.
\(p\)-smoothly equivalent matrix pencils
scientific article; zbMATH DE number 6108779