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

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 
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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 corresponding determinant diagonal matrix diagonalizable digraph dim(ker(L dim(range(L dim(V dimensional vector space dot product eigenspace eigenvalue equal equation Example finite dimensional vector fundamental eigenvectors Gaussian elimination given GramSchmidt Process Hence Hint homogeneous system induction inner product space inverse isomorphism ker(L linear combination linear operator linear system linear transformation linearly independent linearly independent set linearly independent subset n n matrix nonsingular nontrivial nonzero vectors onetoone ordered basis orthogonal basis orthogonal matrix orthonormal basis properties Prove range(L rank(A 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 solution set solve span(S spanning set standard basis Step subspace subspace of Rn Suppose symmetric transition matrix unique unit vector upper triangular vectors in Rn verify zero vector