Determinants and Their Applications in Mathematical Physics
Determinants and Their Applications in Mathematical Physics Robert Vein Paul Dale Springer ...
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Preface The last treatise on the theory of determinants, by T. Muir, revised and enlarged by W.H. Metzler, was published by Dove ...
vi Preface It may well be perfectly legitimate to regard determinant theory as a branch of matrix theory, but it is such a large ...
Preface vii minors ofAnare denoted byM (n) ij , etc., retainer minors are denoted by Nij, etc., simple cofactors are denoted byA ...
viii Preface Maple system on a Macintosh computer, especially in the expansion and factorization of determinants. We are also in ...
Contents ...
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xii Contents ...
Contents xiii 1 Determinants, First Minors, and Cofactors Preface v 1.1 Grassmann Exterior Algebra................. 1.2 Determi ...
xiv Contents 6.10.2 Preparatory Lemmas ................. 287 6.10.3 The Intermediate Solutions.............. 292 6.10.4 Preparat ...
1 Determinants, First Minors, and Cofactors 1.1 Grassmann Exterior Algebra................. LetVbe a finite-dimensional vector s ...
2 1. Determinants, First Minors, and Cofactors It follows from (i) and (ii) that x 1 x 2 ···xn= ∑n k 1 = ··· ∑n kn= a 1 k 1 a 2 ...
1.3 First Minors and Cofactors 3 1.3 First Minors and Cofactors.................. Referring to (1.2.1), put yi=xi−aijej =(ai 1 e ...
4 1. Determinants, First Minors, and Cofactors =(−1) n−i Mij(e ′ 1 ···e ′ j− 1 )(e ′ j ···e ′ n− 1 )ej =(−1) n−i Mij(e 1 ···ej− ...
1.4 The Product of Two Determinants — 1 5 Comparing this result with (1.2.5), |aij|n= n ∑ k= aikAik (1.3.14) which is the expans ...
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