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Normal Forms of a System of Commutative
Matrices That Commute with a Given Matrix
Commutative Subgroups of GLn
9 other sections not shown
algebra N algebra ZPn(a algebras of class annihilator arbitrary field arbitrary matrix assume basis elements basis of Theorem belong Chapter characteristic polynomial coincides commutative algebra Commutative Matrices commutative nilpotent algebra commutative nilpotent subalgebra commutative subgroups completes the proof complex numbers conjugate in Pn Consequently consist of zeros contains a matrix Corollary denote an arbitrary diagonal diagonal matrix direct sum eigenvalues elements are equal equation equivalent field and let follows full linear algebra GL(n indecomposable invariant with respect isomorphic Jordan normal form Let P denote Let us set Let us show linear algebra Pn linearly independent matrices in Pn maximal commutative nilpotent maximal commutative subalgebra minimum polynomial nilpotent matrix nonsingular nonsingular matrix nonzero obtain Obviously operators in Pn Pn of class rank regular representation satisfying condition Schur's lemma signature simultaneously reduced space structural matrices subalgebra of class subalgebra of Pn subspace Q Suppose triangular form triangularly striped vectors