NOTATION GUID E A(a) p(A) r //-matrix Partial matri x Completion o f a partia l matrix Partial Hermitia n Partial positiv e definit e Contraction Partial contractio n Path Circuit Simple circui t Minimal simpl e circui t Chord (o r a circuit ) Chordal grap h Decomposable Complementary principa l submatri x o f A 9 5 resulting fro m deletio n o f th e row s an d columns indicate d b y a . Value of the paramete r a t th e matri x A. 9 7 Set o f matrices whic h agre e wit h respec t t o 9 7 the informatio n t o b e used . Matrix wit h a diagona l multipl e whic h i s 9 9 strictly diagonall y dominant . Rectangular arra y i n which som e entrie s 10 0 are specifie d an d other s ar e unspecified . A specification o f the unspecifie d entries . 10 0 The specifie d diagona l entrie s ar e rea l an d 10 0 if dji i s specified, s o is a^, wit h a%j = aJJ . Partial Hermitia n matri x eac h o f whose 10 1 specified principa l submatrice s i s positiv e definite. Rectangular matri x wit h eac h singula r 10 1 value 1 . Rectangular partia l matri x wit h eac h 10 1 specified submatrice s a contraction . Sequence {{t*i,i 2 }, {*2,*3 },-••, {i*-i,«*}} 10 3 of concatenated edge s (o f a n undirecte d graph). Path wit h i k = i x . 10 3 ii,t2, •,ik-i ar e al l different, an d ik = i\ 10 3 No proper subse t o f vertices i s the se t o f 10 3 vertices o f a simple circuit . Edge whic h joins tw o vertices which ar e no t 10 3 adjacent i n th e circuit . Has no minimal simpl e circuit s o f 4 or more 10 3 edges. nxm partia l matri x A fo r whic h exist s Q\ 10 6 (n-by-n) an d Q2 (m-by-ra ) suc h tha t Q1AQ2 = [BI\ BII] w h e r e t h e off-diagona l blocks consist entirel y o f unspecified entries . aQ(W) Chapter 1 0 The se t { £ Q : W - £ is not invertible} , (spectrum o f W wit h respec t t o th e se t Q) . Il l
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