Linear Algebra (Paperback, 2nd Edition)

LINEAR EQUATIONS1(27)
FIELDS1(2)
SYSTEMS OF LINEAR EQUATIONS3(3)
MATRICES AND ELEMENTARY ROW OPERATIONS6(5)
ROW-REDUCED ECHELON MATRICES11 (5)
MATRIX MULTIPLICATION16 (5)
INVERTIBLE MATRICES21 (7)
VECTOR SPACES28 (39)
VECTOR SPACES28 (6)
SUBSPACES34 (6)
BASES AND DIMENSION40 (9)
COORDINATES49 (6)
SUMMARY OF ROW-EQUIVALENCE55 (3)
COMPUTATIONS CONCERNING SUBSPACES58 (9)
LINEAR TRANSFORMATIONS67 (50)
LINEAR TRANSFORMATIONS67 (7)
THE ALGEBRA OF LINEAR TRANSFORMATIONS74 (10)
ISOMORPHISM84 (2)
REPRESENTATION OF TRANSFORMATIONS BY86 (11)
MATRICES
LINEAR FUNCTIONALS97 (10)
THE DOUBLE DUAL107(4)
THE TRANSPOSE OF A LINEAR TRANSFORMATION111(6)
POLYNOMIALS117(23)
ALGEBRAS117(2)
THE ALGEBRA OF POLYNOMIALS119(5)
LAGRANGE INTERPOLATION124(3)
POLYNOMIAL IDEALS127(7)
THE PRIME FACTORIZATION OF A POLYNOMIAL134(6)
DETERMINANTS140(41)
COMMUTATIVE RINGS140(1)
DETERMINANT FUNCTIONS141(9)
PERMUTATIONS AND THE UNIQUENESS OF150(6)
DETERMINANTS
ADDITIONAL PROPERTIES OF DETERMINANTS156(8)
MODULES164(2)
MULTILINEAR FUNCTIONS166(7)
THE GRASSMAN RING173(8)
ELEMENTARY CANONICAL FORMS181(46)
INTRODUCTION181(1)
CHARACTERISTIC VALUES182(8)
ANNIHILATING POLYNOMIALS190(8)
INVARIANT SUBSPACES198(8)
SIMULTANEOUS TRIANGULATION; SIMULTANEOUS206(3)
DIAGONALIZATION
DIRECT-SUM DECOMPOSITIONS209(4)
INVARIANT DIRECT SUMS213(6)
THE PRIMARY DECOMPOSITION THEOREM219(8)
THE RATIONAL AND JORDAN FORMS227(43)
CYCLIC SUBSPACES AND ANNIHILATORS227(4)
CYCLIC DECOMPOSITIONS AND THE RATIONAL FORM231(13)
THE JORDAN FORM244(7)
COMPUTATION OF INVARIANT FACTORS251(11)
SUMMARY; SEMI-SIMPLE OPERATORS262(8)
INNER PRODUCT SPACES270(49)
INNER PRODUCTS270(7)
INNER PRODUCT SPACES277(13)
LINEAR FUNCTIONALS AND ADJOINTS290(9)
UNITARY OPERATORS299(12)
NORMAL OPERATORS311(8)
OPERATORS ON INNER PRODUCT SPACES319(40)
INTRODUCTION319(1)
FORMS ON INNER PRODUCT SPACES320(5)
POSITIVE FORMS325(7)
MORE ON FORMS332(3)
SPECTRAL THEORY335(14)
FURTHER PROPERTIES OF NORMAL OPERATORS349(10)
BILINEAR FORMS359(27)
BILINEAR FORMS359(8)
SYMMETRIC BILINEAR FORMS367(8)
SKEW-SYMMETRIC BILINEAR FORMS375(4)
GROUPS PRESERVING BILINEAR FORMS379(7)
APPENDIX386(14)
A.1. SETS387(1)
A.2. FUNCTIONS388(3)
A.3. EQUIVALENCE RELATIONS391(3)
A.4. QUOTIENT SPACES394(3)
A.5. EQUIVALENCE RELATIONS IN LINEAR ALGEBRA397(2)
A.6. THE AXIOM OF CHOICE399(1)
BIBLIOGRAPHY400(1)
INDEX401