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Linear algebra 2nd ed

Linear algebra 2nd ed (Loan 28 times)

Material type
단행본
Personal Author
Kwak, Jin Ho , 1948-. Hong, Sungpyo 1948-
Title Statement
Linear algebra / Jin Ho Kwak, Sungpyo Hong.
판사항
2nd ed.
Publication, Distribution, etc
Boston :   Birkhauser ,   c2004.  
Physical Medium
xiv, 390 p. : ill. ; 24 cm.
ISBN
0817642943 (pbk. : alk. paper)
General Note
Includes bibliographical references (p. [383]) and index.  
Subject Added Entry-Topical Term
Algebras, Linear.
000 00802pamuu22002654a 4500
001 000045192952
005 20050923154210
008 040213s2004 maua b 001 0 eng
010 ▼a 2004043751
020 ▼a 0817642943 (pbk. : alk. paper)
040 ▼a DLC ▼c DLC ▼d DLC ▼d 211009
042 ▼a pcc
050 0 0 ▼a QA184.2 ▼b .K93 2004
082 0 0 ▼a 512/.5 ▼2 22
090 ▼a 512.5 ▼b K98L2
100 1 ▼a Kwak, Jin Ho , ▼d 1948-.
245 1 0 ▼a Linear algebra / ▼c Jin Ho Kwak, Sungpyo Hong.
250 ▼a 2nd ed.
260 ▼a Boston : ▼b Birkhauser , ▼c c2004.
300 ▼a xiv, 390 p. : ▼b ill. ; ▼c 24 cm.
500 ▼a Includes bibliographical references (p. [383]) and index.
650 0 ▼a Algebras, Linear.
700 1 ▼a Hong, Sungpyo ▼d 1948-
945 ▼a KINS

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.5 K98L2 Accession No. 121109900 Availability Available Due Date Make a Reservation Service B M
No. 2 Location Science & Engineering Library/Sci-Info(Stacks2)/ Call Number 512.5 K98L2 Accession No. 121175852 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents

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.- 1.9.1 Cryptography.- 1.9.2 Electrical network.- 1.9.3 Leontief model.- 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 Cramer's rule.- 2.5 Applications.- 2.5.1 Miscellaneous examples for determinants.- 2.5.2 Area and volume.- 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.- 3.9.1 Interpolation.- 3.9.2 The Wronskian.- 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.- 4.7.1 Dual spaces and adjoint.- 4.7.2 Computer graphics.- 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.- 5.9.1 Least squares solutions.- 5.9.2 Polynomial approximations 186.- 5.9.3 Orthogonalprojectionmatrices.- 5.10 Exercises.- 6 Diagonalization.- 6.1 Eigenvalues and eigenvectors.- 6.2 Diagonalization of matrices.- 6.3 Applications.- 6.3.1 Linear recurrence relations.- 6.3.2 Linear difference equations.- 6.3.3 Linear differential equations I.- 6.4 Exponential matrices.- 6.5 Applications continued.- 6.5.1 Linear differential equations II.- 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.- 7.5.1 The spectral theorem.- 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.- 8.6.1 The power matrix Ak again.- 8.6.2 The exponential matrix eA again.- 8.6.3 Linear difference equations again.- 8.6.4 Linear differential equations again.- 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.- 9.8.1 Extrema of real-valued functions on ?n.- 9.8.2 Constrained quadratic optimization.- 9.9 Exercises.- Selected Answers and Hints.


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