Author | Kwak, Jin Ho. author |
---|---|
Title | Linear Algebra [electronic resource] / by Jin Ho Kwak, Sungpyo Hong |
Imprint | Boston, MA : Birkhรคuser Boston : Imprint: Birkhรคuser, 2004 |
Edition | Second Edition |
Connect to | http://dx.doi.org/10.1007/978-0-8176-8194-4 |
Descript | XV, 390 p. 9 illus. online resource |
1 Linear Equations and Matrices -- 1.1 Systems of linear equations -- 1.2 Gaussian elimination -- 1.3 Sums and scalar multiplications of matrices -- 1.4 Products of matrices -- 1.5 Block matrices -- 1.6 Inverse matrices -- 1.7 Elementary matrices and finding A?1 -- 1.8 LDU factorization -- 1.9 Applications -- 1.10 Exercises -- 2 Determinants -- 2.1 Basic properties of the determinant -- 2.2 Existence and uniqueness of the determinant -- 2.3 Cofactor expansion -- 2.4 Cramerโs rule -- 2.5 Applications -- 2.6 Exercises -- 3 Vector Spaces -- 3.1 The n-space ?n and vector spaces -- 3.2 Subspaces -- 3.3 Bases -- 3.4 Dimensions -- 3.5 Row and column spaces -- 3.6 Rank and nullity -- 3.7 Bases for subspaces -- 3.8 Invertibility -- 3.9 Applications -- 3.10 Exercises> -- 4 Linear Transformations -- 4.1 Basic propertiesof linear transformations -- 4.2 Invertiblelinear transformations -- 4.3 Matrices of linear transformations -- 4.4 Vector spaces of linear transformations -- 4.5 Change of bases -- 4.6 Similarity -- 4.7. Applications -- 4.8 Exercises -- 5 Inner Product Spaces -- 5.1 Dot products and inner products -- 5.2 The lengths and angles of vectors -- 5.3 Matrix representations of inner products -- 5.4 Gram-Schmidt orthogonalization -- 5.5 Projections -- 5.6 Orthogonal projections -- 5.7 Relations of fundamental subspaces -- 5.8 Orthogonal matrices and isometries -- 5.9 Applications -- 5.10 Exercises -- 6 Diagonalization -- 6.1 Eigenvalues and eigenvectors -- 6.2 Diagonalization of matrices -- 6.3 Applications -- 6.4 Exponential matrices -- 6.5 Applications continued -- 6.6 Diagonalization of linear transformations -- 6.7 Exercises -- 7 Complex Vector Spaces -- 7.1 The n-space ?n and complex vector spaces -- 7.2 Hermitian and unitary matrices -- 7.3 Unitarily diagonalizable matrices -- 7.4 Normal matrices -- 7.5 Application -- 7.6 Exercises -- 8 Jordan Canonical Forms -- 8.1 Basic properties of Jordan canonical forms -- 8.2 Generalized eigenvectors -- 8.3 The power Ak and the exponential eA -- 8.4 Cayley-Hamilton theorem -- 8.5 The minimal polynomial of a matrix> -- 8.6 Applications -- 8.7 Exercises -- 9 Quadratic Forms -- 9.1 Basic properties of quadratic forms -- 9.2 Diagonalization of quadratic forms -- 9.3 A classification of level surfaces -- 9.4 Characterizations of definite forms -- 9.5 Congruence relation -- 9.6 Bilinear and Hermitian forms -- 9.7 Diagonalization of bilinear or Hermitian forms -- 9.8 Applications -- 9.9 Exercises -- Selected Answers and Hints