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A-equivalent matrix A-matrix A-transformations algebra Chap Chapter characteristic roots circle of convergence classical canonical form coefficients consider constant contains defined definition degree deleting denote determinant diagonal matrix elementary divisors elementary transformations elements in F En(X equal equivalent in F example factor of XI—A field F G changes given field H.C.F. of minors H'AH Hence Hermitian i-rowed minors interchange invariant factors ith row jth column latent roots lemma linearly independent matrix of order matrix power series minor of order Moreover multiples non-singular matrix non-zero elements notation null matrix obtained orthogonal matrix polynomial proved radius of convergence rank rational canonical form reciprocal result row or column rows and columns scalar power series sequence of elementary single-column matrix square matrix sufficiently small suffixes suppose symmetrical matrix Theorem 11 typical submatrix unit vector unity variable W. V. D. Hodge x'Ax XI-A