{"product_id":"linear-algebra-isbn-9781119437444","title":"Linear Algebra","description":"\u003cb\u003eLINEAR\u003c\/b\u003e ALGEBRA \u003cp\u003e\u003cb\u003eEXPLORE A COMPREHENSIVE INTRODUCTORY TEXT IN LINEAR ALGEBRA WITH COMPELLING SUPPLEMENTARY MATERIALS, INCLUDING A COMPANION WEBSITE AND SOLUTIONS MANUALS\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e\u003ci\u003eLinear Algebra\u003c\/i\u003e delivers a fulsome exploration of the central concepts in linear algebra, including multidimensional spaces, linear transformations, matrices, matrix algebra, determinants, vector spaces, subspaces, linear independence, basis, inner products, and eigenvectors. While the text provides challenging problems that engage readers in the mathematical theory of linear algebra, it is written in an accessible and simple-to-grasp fashion appropriate for junior undergraduate students.\u003c\/p\u003e \u003cp\u003eAn emphasis on logic, set theory, and functions exists throughout the book, and these topics are introduced early to provide students with a foundation from which to attack the rest of the material in the text. \u003ci\u003eLinear Algebra\u003c\/i\u003e includes accompanying material in the form of a companion website that features solutions manuals for students and instructors. Finally, the concluding chapter in the book includes discussions of advanced topics like generalized eigenvectors, Schur’s Lemma, Jordan canonical form, and quadratic forms. Readers will also benefit from the inclusion of:\u003c\/p\u003e \u003cul\u003e \u003cli\u003eA thorough introduction to logic and set theory, as well as descriptions of functions and linear transformations\u003c\/li\u003e \u003cli\u003eAn exploration of Euclidean spaces and linear transformations between Euclidean spaces, including vectors, vector algebra, orthogonality, the standard matrix, Gauss-Jordan elimination, inverses, and determinants\u003c\/li\u003e \u003cli\u003eDiscussions of abstract vector spaces, including subspaces, linear independence, dimension, and change of basis\u003c\/li\u003e \u003cli\u003eA treatment on defining geometries on vector spaces, including the Gram-Schmidt process\u003c\/li\u003e \u003c\/ul\u003e \u003cp\u003ePerfect for undergraduate students taking their first course in the subject matter, \u003ci\u003eLinear Algebra\u003c\/i\u003e will also earn a place in the libraries of researchers in computer science or statistics seeking an accessible and practical foundation in linear algebra.\u003c\/p\u003e \u003cp\u003ePreface xi\u003c\/p\u003e \u003cp\u003eAcknowledgments xv\u003c\/p\u003e \u003cp\u003eAbout the Companion Website xvi\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Logic and Set Theory 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 Statements 1\u003c\/p\u003e \u003cp\u003eConnectives 2\u003c\/p\u003e \u003cp\u003eLogical Equivalence 3\u003c\/p\u003e \u003cp\u003e1.2 Sets and Quantification 7\u003c\/p\u003e \u003cp\u003eUniversal Quantifiers 8\u003c\/p\u003e \u003cp\u003eExistential Quantifiers 9\u003c\/p\u003e \u003cp\u003eNegating Quantifiers 10\u003c\/p\u003e \u003cp\u003eSet-Builder Notation 12\u003c\/p\u003e \u003cp\u003eSet Operations 13\u003c\/p\u003e \u003cp\u003eFamilies of Sets 14\u003c\/p\u003e \u003cp\u003e1.3 Sets and Proofs 18\u003c\/p\u003e \u003cp\u003eDirect Proof 20\u003c\/p\u003e \u003cp\u003eSubsets 22\u003c\/p\u003e \u003cp\u003eSet Equality 23\u003c\/p\u003e \u003cp\u003eIndirect Proof 24\u003c\/p\u003e \u003cp\u003eMathematical Induction 25\u003c\/p\u003e \u003cp\u003e1.4 Functions 30\u003c\/p\u003e \u003cp\u003eInjections 33\u003c\/p\u003e \u003cp\u003eSurjections 35\u003c\/p\u003e \u003cp\u003eBijections and Inverses 37\u003c\/p\u003e \u003cp\u003eImages and Inverse Images 40\u003c\/p\u003e \u003cp\u003eOperations 41\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Euclidean Space 49\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 Vectors 49\u003c\/p\u003e \u003cp\u003eVector Operations 51\u003c\/p\u003e \u003cp\u003eDistance and Length 57\u003c\/p\u003e \u003cp\u003eLines and Planes 64\u003c\/p\u003e \u003cp\u003e2.2 Dot Product 74\u003c\/p\u003e \u003cp\u003eLines and Planes 77\u003c\/p\u003e \u003cp\u003eOrthogonal Projection 82\u003c\/p\u003e \u003cp\u003e2.3 Cross Product 88\u003c\/p\u003e \u003cp\u003eProperties 91\u003c\/p\u003e \u003cp\u003eAreas and Volumes 93\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Transformations and Matrices 99\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Linear Transformations 99\u003c\/p\u003e \u003cp\u003eProperties 103\u003c\/p\u003e \u003cp\u003eMatrices 106\u003c\/p\u003e \u003cp\u003e3.2 Matrix Algebra 116\u003c\/p\u003e \u003cp\u003eAddition, Subtraction, and Scalar Multiplication 116\u003c\/p\u003e \u003cp\u003eProperties 119\u003c\/p\u003e \u003cp\u003eMultiplication 122\u003c\/p\u003e \u003cp\u003eIdentity Matrix 129\u003c\/p\u003e \u003cp\u003eDistributive Law 132\u003c\/p\u003e \u003cp\u003eMatrices and Polynomials 132\u003c\/p\u003e \u003cp\u003e3.3 Linear Operators 137\u003c\/p\u003e \u003cp\u003eReflections 137\u003c\/p\u003e \u003cp\u003eRotations 142\u003c\/p\u003e \u003cp\u003eIsometries 147\u003c\/p\u003e \u003cp\u003eContractions, Dilations, and Shears 150\u003c\/p\u003e \u003cp\u003e3.4 Injections and Surjections 155\u003c\/p\u003e \u003cp\u003eKernel 155\u003c\/p\u003e \u003cp\u003eRange 158\u003c\/p\u003e \u003cp\u003e3.5 Gauss–Jordan Elimination 162\u003c\/p\u003e \u003cp\u003eElementary Row Operations 164\u003c\/p\u003e \u003cp\u003eSquare Matrices 167\u003c\/p\u003e \u003cp\u003eNonsquare Matrices 171\u003c\/p\u003e \u003cp\u003eGaussian Elimination 177\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Invertibility 183\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Invertible Matrices 183\u003c\/p\u003e \u003cp\u003eElementary Matrices 186\u003c\/p\u003e \u003cp\u003eFinding the Inverse of a Matrix 192\u003c\/p\u003e \u003cp\u003eSystems of Linear Equations 194\u003c\/p\u003e \u003cp\u003e4.2 Determinants 198\u003c\/p\u003e \u003cp\u003eMultiplying a Row by a Scalar 203\u003c\/p\u003e \u003cp\u003eAdding a Multiple of a Row to Another Row 205\u003c\/p\u003e \u003cp\u003eSwitching Rows 210\u003c\/p\u003e \u003cp\u003e4.3 Inverses and Determinants 215\u003c\/p\u003e \u003cp\u003eUniqueness of the Determinant 216\u003c\/p\u003e \u003cp\u003eEquivalents to Invertibility 220\u003c\/p\u003e \u003cp\u003eProducts 222\u003c\/p\u003e \u003cp\u003e4.4 Applications 227\u003c\/p\u003e \u003cp\u003eThe Classical Adjoint 228\u003c\/p\u003e \u003cp\u003eSymmetric and Orthogonal Matrices 229\u003c\/p\u003e \u003cp\u003eCramer’s Rule 234\u003c\/p\u003e \u003cp\u003eLU Factorization 236\u003c\/p\u003e \u003cp\u003eArea and Volume 238\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Abstract Vectors 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Vector Spaces 245\u003c\/p\u003e \u003cp\u003eExamples of Vector Spaces 247\u003c\/p\u003e \u003cp\u003eLinear Transformations 253\u003c\/p\u003e \u003cp\u003e5.2 Subspaces 259\u003c\/p\u003e \u003cp\u003eExamples of Subspaces 260\u003c\/p\u003e \u003cp\u003eProperties 261\u003c\/p\u003e \u003cp\u003eSpanning Sets 264\u003c\/p\u003e \u003cp\u003eKernel and Range 266\u003c\/p\u003e \u003cp\u003e5.3 Linear Independence 272\u003c\/p\u003e \u003cp\u003eEuclidean Examples 274\u003c\/p\u003e \u003cp\u003eAbstract Vector Space Examples 276\u003c\/p\u003e \u003cp\u003e5.4 Basis and Dimension 281\u003c\/p\u003e \u003cp\u003eBasis 281\u003c\/p\u003e \u003cp\u003eZorn’s Lemma 285\u003c\/p\u003e \u003cp\u003eDimension 287\u003c\/p\u003e \u003cp\u003eExpansions and Reductions 290\u003c\/p\u003e \u003cp\u003e5.5 Rank and Nullity 296\u003c\/p\u003e \u003cp\u003eRank-Nullity Theorem 297\u003c\/p\u003e \u003cp\u003eFundamental Subspaces 302\u003c\/p\u003e \u003cp\u003eRank and Nullity of a Matrix 304\u003c\/p\u003e \u003cp\u003e5.6 Isomorphism 310\u003c\/p\u003e \u003cp\u003eCoordinates 315\u003c\/p\u003e \u003cp\u003eChange of Basis 320\u003c\/p\u003e \u003cp\u003eMatrix of a Linear Transformation 324\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Inner Product Spaces 335\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Inner Products 335\u003c\/p\u003e \u003cp\u003eNorms 341\u003c\/p\u003e \u003cp\u003eMetrics 342\u003c\/p\u003e \u003cp\u003eAngles 344\u003c\/p\u003e \u003cp\u003eOrthogonal Projection 347\u003c\/p\u003e \u003cp\u003e6.2 Orthonormal Bases 352\u003c\/p\u003e \u003cp\u003eOrthogonal Complement 355\u003c\/p\u003e \u003cp\u003eDirect Sum 357\u003c\/p\u003e \u003cp\u003eGram–Schmidt Process 361\u003c\/p\u003e \u003cp\u003eQR Factorization 366\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Matrix Theory 373\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 Eigenvectors and Eigenvalues 373\u003c\/p\u003e \u003cp\u003eEigenspaces 375\u003c\/p\u003e \u003cp\u003eCharacteristic Polynomial 377\u003c\/p\u003e \u003cp\u003eCayley–Hamilton Theorem 382\u003c\/p\u003e \u003cp\u003e7.2 Minimal Polynomial 386\u003c\/p\u003e \u003cp\u003eInvariant Subspaces 389\u003c\/p\u003e \u003cp\u003eGeneralized Eigenvectors 391\u003c\/p\u003e \u003cp\u003ePrimary Decomposition Theorem 393\u003c\/p\u003e \u003cp\u003e7.3 Similar Matrices 402\u003c\/p\u003e \u003cp\u003eSchur’s Lemma 405\u003c\/p\u003e \u003cp\u003eBlock Diagonal Form 408\u003c\/p\u003e \u003cp\u003eNilpotent Matrices 412\u003c\/p\u003e \u003cp\u003eJordan Canonical Form 415\u003c\/p\u003e \u003cp\u003e7.4 Diagonalization 422\u003c\/p\u003e \u003cp\u003eOrthogonal Diagonalization 426\u003c\/p\u003e \u003cp\u003eSimultaneous Diagonalization 428\u003c\/p\u003e \u003cp\u003eQuadratic Forms 432\u003c\/p\u003e \u003cp\u003eFurther Reading 441\u003c\/p\u003e \u003cp\u003eIndex 443\u003c\/p\u003e \u003cp\u003e\u003cb\u003eMICHAEL L. O’LEARY,\u003c\/b\u003e is Professor of Mathematics at College of DuPage in Glen Ellyn, Illinois. He received his doctoral degree in mathematics from the University of California, Irvine in 1994 and is the author of \u003ci\u003eA First Course in Mathematical Logic and Set Theory and Revolutions of Geometry\u003c\/i\u003e, both published by Wiley.\u003c\/p\u003e  \u003cp\u003e\u003cb\u003eEXPLORE A COMPREHENSIVE INTRODUCTORY TEXT IN LINEAR ALGEBRA WITH COMPELLING SUPPLEMENTARY MATERIALS, INCLUDING A COMPANION WEBSITE AND SOLUTIONS MANUALS\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003e\u003ci\u003eLinear Algebra\u003c\/i\u003e delivers a fulsome exploration of the central concepts in linear algebra, including multidimensional spaces, linear transformations, matrices, matrix algebra, determinants, vector spaces, subspaces, linear independence, basis, inner products, and eigenvectors. While the text provides challenging problems that engage readers in the mathematical theory of linear algebra, it is written in an accessible and simple-to-grasp fashion appropriate for junior undergraduate students.\u003c\/p\u003e\u003cp\u003eAn emphasis on logic, set theory, and functions exists throughout the book, and these topics are introduced early to provide students with a foundation from which to attack the rest of the material in the text. \u003ci\u003eLinear Algebra\u003c\/i\u003e includes accompanying material in the form of a companion website that features solutions manuals for students and instructors. Finally, the concluding chapter in the book includes discussions of advanced topics like generalized eigenvectors, Schur’s Lemma, Jordan canonical form, and quadratic forms. Readers will also benefit from the inclusion of:\u003c\/p\u003e\u003cul\u003e\n\u003cli\u003eA thorough introduction to logic and set theory, as well as descriptions of functions and linear transformations\u003c\/li\u003e\n\u003cli\u003eAn exploration of Euclidean spaces and linear transformations between Euclidean spaces, including vectors, vector algebra, orthogonality, the standard matrix, Gauss-Jordan elimination, inverses, and determinants\u003c\/li\u003e\n\u003cli\u003eDiscussions of abstract vector spaces, including subspaces, linear independence, dimension, and change of basis\u003c\/li\u003e\n\u003cli\u003eA treatment on defining geometries on vector spaces, including the Gram-Schmidt process\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003ePerfect for undergraduate students taking their first course in the subject matter, \u003ci\u003eLinear Algebra\u003c\/i\u003e will also earn a place in the libraries of researchers in computer science or statistics seeking an accessible and practical foundation in linear algebra.\u003c\/p\u003e","brand":"Wiley","offers":[{"title":"Default Title","offer_id":47989531312357,"sku":"NP9781119437444","price":123.95,"currency_code":"USD","in_stock":false}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/1842\/7735\/files\/9781119437444.jpg?v=1761784484","url":"https:\/\/k12savings.com\/products\/linear-algebra-isbn-9781119437444","provider":"K12savings","version":"1.0","type":"link"}