vi Content s 5 Invarian t Subspaces 8 5 5.1 Th e characteristic polynomial 8 5 5.2 Invarian t subspaces 8 8 5.3 Th e minimal polynomial 9 3 6 Inner-Produc t Spaces 10 3 6.1 Inne r products 10 3 6.2 Dualit y and the adjoint Il l 6.3 Self-adjoin t operator s 11 3 6.4 Norma l operators 11 9 6.5 Unitar y and orthogonal operators 12 1 *6.6 Positiv e definite operators 12 7 *6.7 Pola r decomposition 12 8 *6.8 Contraction s and unitary dilations 13 2 7 Structur e Theorems 13 5 7.1 Reducin g subspaces 13 5 7.2 Semisimpl e systems 14 2 7.3 Nilpoten t operators 14 7 7.4 Th e Jordan canonical form 15 1 *7.5 Th e cyclic decomposition, general case 15 2 *7.6 Th e Jordan canonical form, general case 15 6 8 Additiona l Topics 15 9 8.1 Function s of an operator 15 9 8.2 Quadrati c forms 16 2 8.3 Perron-Frobeniu s theory 16 6 8.4 Stochasti c matrices 17 8 8.5 Representatio n of finite groups 18 0 A Appendi x 18 7 A.l Equivalenc e relations-partitions 18 7 A.2 Map s 18 8 A.3 Group s 18 9 *A.4 Grou p actions 19 4 A.5 Ring s and algebras 19 6
Previous Page Next Page