Linear Algebra with ApplicationsRenowned for its thoroughness and accessibility, this best-selling text by one of the leading figures in linear algebra reform offers students a challenging yet enjoyable study of linear algebra that is infused with an abundance of applications. Balancing coverage of mathematical theory and applied topics, it takes extra care in explaining concepts clearly so that students at a variety of levels can read and understand the material. Numerous worked examples are integrated throughout the text. This revision stresses the important roles played by geometry and visualization in linear algebra. ATLAST Computer Exercises for Linear Algebra a project manual using MATLAB--may be packaged free with the text. |
Contents
MATRICES AND SYSTEMS OF EQUATIONS | 1 |
DETERMINANTS | 84 |
VECTOR SPACES | 108 |
Copyright | |
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a₁ A₂ b₁ b₂ c₁ c₂ coefficient matrix column space column vectors condition number coordinate vector corresponding defined denote det(A determine e₁ e₂ eigenvalues eigenvector belonging eigenvectors elementary matrix elements entries equation EXAMPLE Exercise factorization Figure floating-point follows function given graph hence Householder transformation inner product space least squares problem linear combination linear operator linear system linear transformation linearly independent m x n MATLAB MATLAB to compute n x n matrix N(AT nonsingular matrix nonzero vectors ordered basis orthogonal matrix orthonormal basis orthonormal set P₁ positive definite PROOF R(AT real numbers reduced row echelon relative error respect row echelon form row equivalent row operation scalar multiplication Section Show singular value decomposition solution subspace symmetric system Ax Theorem transition matrix u₁ u₂ upper triangular V₁ V₂ vector space verify x₁ y₁ Y₂ zero λ₁ λ₂