Elementary Linear Algebra: Applications VersionElementary Linear Algebra 10th edition gives an elementary treatment of linear algebra that is suitable for a first course for undergraduate students. The aim is to present the fundamentals of linear algebra in the clearest possible way; pedagogy is the main consideration. Calculus is not a prerequisite, but there are clearly labeled exercises and examples (which can be omitted without loss of continuity) for students who have studied calculus. Technology also is not required, but for those who would like to use MATLAB, Maple, or Mathematica, or calculators with linear algebra capabilities, exercises are included at the ends of chapters that allow for further exploration using those tools. |
Contents
CONTENTS | 2 |
43 | 25 |
xvi | 119 |
General Vector Spaces | 171 |
Eigenvalues and Eigenvectors | 295 |
Inner Product Spaces | 335 |
Diagonalization and Quadratic Forms | 389 |
Linear Transformations | 433 |
CHAPTER 9 | 477 |
Applications of Linear Algebra | 519 |
APPENDIX A How to Read Theorems | 711 |
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Common terms and phrases
3-space angle augmented matrix axioms basis vectors called Chapter 1 Systems cofactor expansion column space column vectors components compute coordinate vector corresponding defined DEFINITION denote det(A determinant dot product eigenvalues eigenvector elementary matrices elementary row operations entries Equations and Matrices Euclidean inner product EXAMPLE expressed Figure following theorem Formula geometric inner product space invertible matrix justify your answer linear combination Linear Equations linear system linear system Ax linear transformation linearly independent linearly independent set matrix operator matrix transformation nonzero vector null space obtained one-to-one orthogonal projection orthonormal plane polynomial Proof properties Prove real numbers reduced row echelon result rotation row echelon form row space row vectors scalar multiplication set of vectors solve span square matrix standard basis standard matrix subspace symmetric matrix Systems of Linear transition matrix True-False Exercises u₁ unit vectors upper triangular v₁ vectors in Rn verify