Elementary Linear Algebra: Applications VersionElementary Linear Algebra: Applications Version, 11th 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. |
Contents
CONTENTS | 2 |
8 | 75 |
Determinants | 105 |
Euclidean Vector Spaces | 131 |
General Vector Spaces | 183 |
Eigenvalues and Eigenvectors | 291 |
Inner Product Spaces | 345 |
Diagonalization and Quadratic Forms | 401 |
General Linear Transformations | 447 |
Numerical Methods | 491 |
Applications of Linear Algebra | 528 |
8 | 588 |
9 | 595 |
APPENDIX A Working with Proofs | A-1 |
is embodied in the matrix | A-3 |
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Common terms and phrases
algebra angle axioms basis vectors Calculus required called Chapter cofactor expansion column space column vectors compute coordinate vector corresponding defined definition denote det(A determine diagonalizable dot product eigenspace eigenvalues eigenvector entries Euclidean inner product EXAMPLE Exercise Set expressed factor Figure following theorem Formula functions geometric inner product space invertible matrix justify your answer least squares linear combination linear operator linear system linear transformation linearly independent LU-decomposition matrix operator matrix transformation nonzero vector null space obtain one-to-one orthogonal matrix orthogonal projection orthonormal basis P₁ plane points polynomial positive Proof Prove quadratic form real numbers reduced row echelon result rotation row echelon form row space row vectors scalar multiplication set of vectors singular value solve span square matrix standard basis standard matrix subspace symmetric matrix T₁ transition matrix u₁ unit vector v₁ vector space verify w₁ x-axis x₁ zero