Elementary Linear AlgebraElementary Linear Algebra develops and explains in careful detail the computational techniques and fundamental theoretical results central to a first course in linear algebra. This highly acclaimed text focuses on developing the abstract thinking essential for further mathematical study The authors give early, intensive attention to the skills necessary to make students comfortable with mathematical proofs. The text builds a gradual and smooth transition from computational results to general theory of abstract vector spaces. It also provides flexbile coverage of practical applications, exploring a comprehensive range of topics. Ancillary list:* Maple Algorithmic testing- Maple TA- www.maplesoft.com - Includes a wide variety of applications, technology tips and exercises, organized in chart format for easy reference - More than 310 numbered examples in the text at least one for each new concept or application - Exercise sets ordered by increasing difficulty, many with multiple parts for a total of more than 2135 questions - Provides an early introduction to eigenvalues/eigenvectors - A Student solutions manual, containing fully worked out solutions and instructors manual available |
Contents
1 | |
Chapter 2 Systems of Linear Equations | 79 |
Chapter 3 Determinants and Eigenvalues | 143 |
Chapter 4 Finite Dimensional Vector Spaces | 203 |
Chapter 5 Linear Transformations | 305 |
Chapter 6 Orthogonality | 397 |
Chapter 7 Complex Vector Spaces and General Inner Products | 445 |
Chapter 8 Additional Applications | 491 |
Chapter 9 Numerical Methods | 587 |
Other editions - View all
Elementary Linear Algebra Stephen Francis Andrilli,Stephen Andrilli,David Hecker No preview available - 2010 |
Common terms and phrases
algebraic multiplicity angle augmented matrix calculate codomain coefficient Consider coordinates coordinatization corresponding d₁ determinant diagonal matrix diagonalizable digraph dim(ker(L dim(range(L dim(V dim(W dimensional vector space dot product eigenspace eigenvalue eigenvectors equal equation Example finite dimensional vector fundamental eigenvectors Gaussian elimination given Gram-Schmidt Process Hence Hint homogeneous system induction inner product space inverse isomorphism ker(L L₁ linear combination linear operator linear system linear transformation linearly independent linearly independent set linearly independent subset nonsingular nontrivial nonzero vectors obtain one-to-one ordered basis orthogonal basis orthogonal matrix orthonormal basis plane projwv properties Prove range(L real numbers reduced row echelon respect rotation row echelon form row equivalent row operation row reducing row space scalar multiplication set of vectors singular values singular vectors solution set solve span(S spanning set standard basis Step subspace Suppose symmetric transition matrix unique unit vector upper triangular verify zero vector