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Introduction to linear algebra

ผู้แต่ง: Gilbert Strang
สำนักพิมพ์: Wellesley, MA : Wellesley-Cambridge Press, ©2009.
ครั้งที่พิมพ์/รูปแบบ:   หนังสือ : ภาษาอังกฤษ : 4th edดูครั้งที่พิมพ์และรูปแบบ
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Book Description: Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course  อ่านมากขึ้น…
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ขนิดวัสดุ: ทรัพยากรอินแทอร์เน็ต
ประเภทของเอกสาร: หนังสือ, แหล่งข้อมูลอินเทอร์เน็ต
ผู้แต่งทั้งหมด : ผู้แต่งร่วม Gilbert Strang
ISBN: 9780980232714 0980232716 9780980232721 0980232724
OCLC Number: 298178914
หมายเหตุ: Includes index.
คำอธิบาย: ix, 574 pages : illustrations ; 24 cm
สารบัญ: 1: Introduction To Vectors: --
1-1: Vectors and linear combinations --
1-2: Lengths and dot products --
1-3: Matrices --
2: Solving Linear Equations: --
2-1: Vectors and linear equations --
2-2: Idea of elimination --
2-3: Elimination using matrices --
2-4: Rules for matrix operations --
2-5: Inverse matrices --
2-6: Elimination = factorization: A = LU --
2-7: Transposes and permutations --
3: Vector Spaces And Subspaces: --
3-1: Spaces of vectors --
3-2: Nullspace of A: Solving Ax = 0 --
3-3: Rank and the row reduced form --
3-4: Complete solution to Ax = b --
3-5: Independence, basis and dimension --
3-6: Dimensions of the four subspaces --
4: Orthogonality: --
4-1: Orthogonality of the four subspaces --
4-2: Projections --
4-3: Least squares approximations --
4-4: Orthogonal bases and gram-Schmidt --
5: Determinants --
5-1: Properties of determinants --
5-2: Permutations and cofactors --
5-3: Cramer's rule, inverses, and volumes --
6: Eigenvalues And Eigenvectors: --
6-1: Introduction to eigenvalues --
6-2: Diagonalizing a matrix --
6-3: Applications to differential equations --
6-4: Symmetric matrices --
6-5: Positive definite matrices --
6-6: Similar matrices --
6-7: Singular Value Decomposition (SVD) --
7: Linear Transformations: --
7-1: Idea of a linear transformation --
7-2: Matrix of a linear transformation --
7-3: Diagonalization and the pseudoinverse --
8: Applications: --
8-1: Matrices in engineering --
8-2: Graphs and networks --
8-3: Markov matrices, population, and economics --
8-4: Linear programming --
8-5: Fourier series: linear algebra for functions --
8-6: Linear algebra for statistics and probability --
8-7: Computer graphics --
9: Numerical Linear Algebra: --
9-1: Gaussian elimination in practice --
9-2: Norms and condition numbers --
9-3: Iterative methods and preconditioners --
10: Complex vectors and matrices --
10-1: Complex numbers --
10-2: Hermitian and unitary matrices --
10-3: Fast Fourier transform --
Solutions to selected exercises --
Conceptual questions for review --
Glossary: A dictionary for linear algebra --
Matrix factorizations --
Teaching codes --
Index --
Linear algebra in a nutshell.
ความรับผิดชอบ: Gilbert Strang.

บทคัดย่อ:

Book Description: Gilbert Strang's textbooks have changed the entire approach to learning linear algebra -- away from abstract vector spaces to specific examples of the four fundamental subspaces: the column space and nullspace of A and A'. Introduction to Linear Algebra, Fourth Edition includes challenge problems to complement the review problems that have been highly praised in previous editions. The basic course is followed by seven applications: differential equations, engineering, graph theory, statistics, Fourier methods and the FFT, linear programming, and computer graphics. Thousands of teachers in colleges and universities and now high schools are using this book, which truly explains this crucial subject.

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