000			06813cam a22003014a 4500
008			080402s2005 nyua b 001 0 eng
010			_a2005040244
020			_a0387247661
020			_a9780387247663
035			_a(Sirsi) u499
040			_aEG-CaNU _cEG-CaNU _dEG-CaNU
042			_ancode
082	0	0	_a512.5 _2 22
100	1		_aRoman, Steven. _94737
245	1	0	_aAdvanced linear algebra / _c Steven Roman.
250			_a2nd ed.
260			_aNew York : _b Springer, _c c2005.
300			_axvi, 482 p. : _b ill. ; _c 25 cm.
490	0		_aGraduate texts in mathematics ; _v 135
504			_aIncludes bibliographical references (p. [473]-474) and index.
505	0		_g Ch. 0. _t Preliminaries -- _g Pt. 1. _t Preliminaries -- _t Matrices -- _t Determinants -- _t Polynomials. Functions -- _t Equivalence Relations -- _t Zorn’s Lemma -- _t Cardinality -- _g Pt. 2. _t Algebraic Structures -- _t Groups -- _t Rings -- _t Integral Domains -- _t Ideals and Principal Ideal Domains -- _t Prime Elements -- _t Fields -- _t The Characteristic of a Ring -- _g Pt. 1. _t Basic Linear Algebra -- _g Ch. 1. _t Vector Spaces -- _t Vector Spaces -- _t Subspaces -- _t The Lattice of Subspaces -- _t Direct Sums -- _t Spanning Sets and Linear Independence -- _t The Dimension of a Vector Space -- _t The Row and Column Space of a Matrix -- _t Coordinate Matrices -- _t Exercises -- _g Ch. 2. _t Linear Transformations -- _t Linear Transformations -- _t The Kernel and Image of a Linear Transformation -- _t Isomorphisms -- _t The Rank Plus Nullity Theorem -- _t Linear Transformations from F[superscript n] to F[superscript m] -- _t Change of Basis Matrices -- _t The Matrix of a Linear Transformation -- _t Change of Bases for Linear Transformations -- _t Equivalence of Matrices -- _t Similarity of Matrices -- _t Invariant Subspaces and Reducing Pairs -- _t Exercises -- _g Ch. 3. _t Isomorphism Theorems -- _t Quotient Spaces -- _t The First Isomorphism Theorem -- _t The Dimension of a Quotient Space -- _t Additional Isomorphism Theorems -- _t Linear Functionals -- _t Dual Bases -- _t Reflexivity -- _t Annihilators -- _t Operator Adjoints -- _t Exercises -- _g Ch. 4. _t Modules I -- _t Motivation -- _t Modules -- _t Submodules -- _t Direct Sums -- _t Spanning Sets -- _t Linear Independence -- _t Homomorphisms -- _t Free Modules -- _t Summary -- _t Exercises -- _g Ch. 5. _t Modules II -- _t Quotient Modules -- _t Quotient Rings and Maximal Ideals -- _t Noetherian Modules -- _t The Hilbert Basis Theorem -- _t Exercises -- _g Ch. 6. _t Modules over Principal Ideal Domains -- _t Free Modules over a Principal Ideal Domain -- _t Torsion Modules -- _t The Primary Decomposition Theorem -- _t The Cyclic Decomposition Theorem for Primary Modules -- _t Uniqueness -- _t The Cyclic Decomposition Theorem -- _t Exercises -- _g Ch. 7. _t Structure of a Linear Operator -- _t A Brief Review -- _t The Module Associated with a Linear Operator -- _t Submodules and Invariant Subspaces -- _t Orders and the Minimal Polynomial -- _t Cyclic Submodules and Cyclic Subspaces -- _t Summary -- _t The Decomposition of V. -- _t The Rational Canonical Form -- _t Exercises -- _g Ch. 8. _t Eigenvalues and Eigenvectors -- _t The Characteristic Polynomial of an Operator -- _t Eigenvalues and Eigenvectors -- _t The Cayley-Hamilton Theorem -- _t The Jordan Canonical Form -- _t Geometric and Algebraic Multiplicities -- _t Diagonalizable Operators -- _t Projections -- _t The Algebra of Projections -- _t Resolutions of the Identity -- _t Projections and Diagonalizability -- _t Projections and Invariance -- _t Exercises -- _g Ch. 9. _t Real and Complex Inner Product Spaces -- _t Introduction -- _t Norm and Distance -- _t Isometries -- _t Orthogonality -- _t Orthogonal and Orthonormal Sets -- _t The Projection Theorem -- _t The Gram-Schmidt Orthogonalization Process -- _t The Riesz Representation Theorem -- _t Exercises -- _g Ch. 10. _t Spectral Theorem for Normal Operators -- _t The Adjoint of a Linear Operator -- _t Orthogonal Diagonalizability -- _t Motivation -- _t Self-Adjoint Operators -- _t Unitary Operators -- _t Normal Operators -- _t Orthogonal Diagonalization -- _t Orthogonal Projections -- _t Orthogonal Resolutions of the Identity -- _t The Spectral Theorem -- _t Functional Calculus -- _t Positive Operators -- _t The Polar Decomposition of an Operator -- _t Exercises -- _g Pt. 2. _t Topics -- _g Ch. 11. _t Metric Vector Spaces -- _t Symmetric, Skew-symmetric and Alternate Forms -- _t The Matrix of a Bilinear Form -- _t Quadratic Forms -- _t Linear Functionals -- _t Orthogonality -- _t Orthogonal Complements -- _t Orthogonal Direct Sums -- _t Quotient Spaces -- _t Symplectic Geometry - Hyperbolic Planes -- _t Orthogonal Geometry - Orthogonal Bases -- _t The Structure of an Orthogonal Geometry -- _t Isometries -- _t Symmetries -- _t Witt’s Cancellation Theorem -- _t Witt’s Extension Theorem -- _t Maximum Hyperbolic Subspaces -- _t Exercises -- _g Ch. 12. _t Metric Spaces -- _t The Definition -- _t Open and Closed Sets -- _t Convergence in a Metric Space -- _t The Closure of a Set -- _t Dense Subsets -- _t Continuity -- _t Completeness -- _t Isometries -- _t The Completion of a Metric Space -- _t Exercises -- _g Ch. 13. _t Hilbert Spaces -- _t A Brief Review -- _t Hilbert Spaces -- _t Infinite Series -- _t An Approximation Problem -- _t Hilbert Bases -- _t Fourier Expansions -- _t A Characterization of Hilbert Bases -- _t Hilbert Dimension -- _t A Characterization of Hilbert Spaces -- _t The Riesz Representation Theorem -- _t Exercises -- _g Ch. 14. _t Tensor Products -- _t Free Vector Spaces -- _t Another Look at the Direct Sum -- _t Bilinear Maps and Tensor Products -- _t Properties of the Tensor Product -- _t The Tensor Product of Linear Transformations -- _t Change of Base Field -- _t Multilinear Maps and Iterated Tensor Products -- _t Alternating Maps and Exterior Products -- _t Exercises -- _g Ch. 15. _t Affine Geometry -- _t Affine Geometry -- _t Affine Combinations -- _t Affine Hulls -- _t The Lattice of Flats -- _t Affine Independence -- _t Affine Transformations -- _t Projective Geometry -- _t Exercises -- _g Ch. 16. _t Umbral Calculus -- _t Formal Power Series -- _t The Umbral Algebra -- _t Formal Power Series as Linear Operators -- _t Sheffer Sequences -- _t Examples of Sheffer Sequences -- _t Umbral Operators and Umbral Shifts -- _t Continuous Operators on the Umbral Algebra -- _t Operator Adjoints -- _t Automorphisms of the Umbral Algebra -- _t Derivations of the Umbral Algebra -- _t Exercises.
630	0	0	_aCIT. _914
630	0	0	_aMOT. _99971
630	0	0	_aITS. _9160
650		0	_aAlgebras, Linear. _9930
596			_a1
999			_c3987 _d3987