 Chapter 1: Systems of Linear Equations
 Chapter 1.1: Introduction to Systems of Linear Equations
 Chapter 1.2: Gaussian Elimination and GaussJordan Elimination
 Chapter 1.3: Applications of Systems of Linear Equations
 Chapter 2: Matrices
 Chapter 2.1: Operations with Matrices
 Chapter 2.2: Properties of Matrix Operations
 Chapter 2.3: The Inverse of a Matrix
 Chapter 2.4: Elementary Matrices
 Chapter 2.5: Applications of Matrix Operations
 Chapter 3: Determinants
 Chapter 3.1: The Determinant of a Matrix
 Chapter 3.2: Evaluation of a Determinant Using Elementary Operations
 Chapter 3.3: Properties of Determinants
 Chapter 3.4: Introduction to Eigenvalues
 Chapter 3.5: Applications of Determinants
 Chapter 4: Vector Spaces
 Chapter 4.1: Vectors in Rn
 Chapter 4.2: Vector Spaces
 Chapter 4.3: Subspaces of Vector Spaces
 Chapter 4.4: Spanning Sets and Linear Independence
 Chapter 4.5: Basis and Dimension
 Chapter 4.6: Rank of a Matrix and Systems of Linear Equations
 Chapter 4.7: Coordinates and Change of Basis
 Chapter 4.8: Applications of Vector Spaces
 Chapter 5: Inner Product Spaces
 Chapter 5.1: Length and Dot Product in Rn
 Chapter 5.2: Inner Product Spaces
 Chapter 5.3: Orthonormal Bases: GramSchmidt Process
 Chapter 5.4: Mathematical Models and Least Squares Analysis
 Chapter 5.5: Applications of Inner Product Spaces
 Chapter 6: Linear Transformations
 Chapter 6.1: Introduction to Linear Transformations
 Chapter 6.2: The Kernel and Range of a Linear Transformation
 Chapter 6.3: Matrices for Linear Transformations
 Chapter 6.4: Transition Matrices and Similarity
 Chapter 6.5: Applications of Linear Transformations
 Chapter 7: Eigenvalues and Eigenvectors
 Chapter 7.1: Eigenvalues and Eigenvectors
 Chapter 7.2: Diagonalization
 Chapter 7.3: Symmetric Matrices and Orthogonal Diagonalization
 Chapter 7.4: Applications of Eigenvalues and Eigenvectors
 Chapter Appendix: Mathematical Induction and Other Forms of Proofs
Elementary Linear Algebra 6th Edition  Solutions by Chapter
Full solutions for Elementary Linear Algebra  6th Edition
ISBN: 9780618783762
Elementary Linear Algebra  6th Edition  Solutions by Chapter
Get Full SolutionsElementary Linear Algebra was written by and is associated to the ISBN: 9780618783762. The full stepbystep solution to problem in Elementary Linear Algebra were answered by , our top Math solution expert on 03/13/18, 08:31PM. This expansive textbook survival guide covers the following chapters: 43. This textbook survival guide was created for the textbook: Elementary Linear Algebra, edition: 6. Since problems from 43 chapters in Elementary Linear Algebra have been answered, more than 13662 students have viewed full stepbystep answer.

Back substitution.
Upper triangular systems are solved in reverse order Xn to Xl.

Circulant matrix C.
Constant diagonals wrap around as in cyclic shift S. Every circulant is Col + CIS + ... + Cn_lSn  l . Cx = convolution c * x. Eigenvectors in F.

Complex conjugate
z = a  ib for any complex number z = a + ib. Then zz = Iz12.

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Incidence matrix of a directed graph.
The m by n edgenode incidence matrix has a row for each edge (node i to node j), with entries 1 and 1 in columns i and j .

Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.

Nilpotent matrix N.
Some power of N is the zero matrix, N k = o. The only eigenvalue is A = 0 (repeated n times). Examples: triangular matrices with zero diagonal.

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Nullspace matrix N.
The columns of N are the n  r special solutions to As = O.

Outer product uv T
= column times row = rank one matrix.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Pivot columns of A.
Columns that contain pivots after row reduction. These are not combinations of earlier columns. The pivot columns are a basis for the column space.

Projection matrix P onto subspace S.
Projection p = P b is the closest point to b in S, error e = b  Pb is perpendicularto S. p 2 = P = pT, eigenvalues are 1 or 0, eigenvectors are in S or S...L. If columns of A = basis for S then P = A (AT A) 1 AT.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular Value Decomposition
(SVD) A = U:E VT = (orthogonal) ( diag)( orthogonal) First r columns of U and V are orthonormal bases of C (A) and C (AT), AVi = O'iUi with singular value O'i > O. Last columns are orthonormal bases of nullspaces.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.

Volume of box.
The rows (or the columns) of A generate a box with volume I det(A) I.