- Chapter 1: MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS
- Chapter 1.1: MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS
- Chapter 1.2: MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS
- Chapter 1.3: MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS
- Chapter 1.4: MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS
- Chapter 1.5: MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS
- Chapter 1.6: MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS
- Chapter 1.7: MATRICES, VECTORS, AND SYSTEMS OF LINEAR EQUATIONS
- Chapter 2: MATRICES AND LINEAR TRANSFORMATIONS
- Chapter 2.1: MATRICES AND LINEAR TRANSFORMATIONS
- Chapter 2.2: MATRICES AND LINEAR TRANSFORMATIONS
- Chapter 2.3: MATRICES AND LINEAR TRANSFORMATIONS
- Chapter 2.4: MATRICES AND LINEAR TRANSFORMATIONS
- Chapter 2.5: MATRICES AND LINEAR TRANSFORMATIONS
- Chapter 2.6: MATRICES AND LINEAR TRANSFORMATIONS
- Chapter 2.7: MATRICES AND LINEAR TRANSFORMATIONS
- Chapter 2.8: MATRICES AND LINEAR TRANSFORMATIONS
- Chapter 3: DETERMINANTS
- Chapter 3.1: DETERMINANTS
- Chapter 3.2: DETERMINANTS
- Chapter 4: DETERMINANTS
- Chapter 4.1: SUBSPACES AND THEIR PROPERTIES
- Chapter 4.2: SUBSPACES AND THEIR PROPERTIES
- Chapter 4.3: SUBSPACES AND THEIR PROPERTIES
- Chapter 4.4: DETERMINANTS
- Chapter 4.5: DETERMINANTS
- Chapter 5: EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION
- Chapter 5.1: EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION
- Chapter 5.2: EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION
- Chapter 5.3: EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION
- Chapter 5.4: EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION
- Chapter 5.5: EIGENVALUES, EIGENVECTORS, AND DIAGONALIZATION
- Chapter 6.1: ORTHOGONALITY
- Chapter 6.2: ORTHOGONALITY
Elementary Linear Algebra: A Matrix Approach 2nd Edition - Solutions by Chapter
Full solutions for Elementary Linear Algebra: A Matrix Approach | 2nd Edition
ISBN: 9780131871410
Elementary Linear Algebra: A Matrix Approach | 2nd Edition - Solutions by Chapter
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This textbook survival guide was created for the textbook: Elementary Linear Algebra: A Matrix Approach, edition: 2. Elementary Linear Algebra: A Matrix Approach was written by and is associated to the ISBN: 9780131871410. Since problems from 34 chapters in Elementary Linear Algebra: A Matrix Approach have been answered, more than 101475 students have viewed full step-by-step answer. This expansive textbook survival guide covers the following chapters: 34. The full step-by-step solution to problem in Elementary Linear Algebra: A Matrix Approach were answered by , our top Math solution expert on 12/27/17, 07:57PM.
Key Math Terms and definitions covered in this textbook
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Cramer's Rule for Ax = b.
B j has b replacing column j of A; x j = det B j I det A
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Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].
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Dimension of vector space
dim(V) = number of vectors in any basis for V.
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Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.
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Echelon matrix U.
The first nonzero entry (the pivot) in each row comes in a later column than the pivot in the previous row. All zero rows come last.
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Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.
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Incidence matrix of a directed graph.
The m by n edge-node incidence matrix has a row for each edge (node i to node j), with entries -1 and 1 in columns i and j .
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Krylov subspace Kj(A, b).
The subspace spanned by b, Ab, ... , Aj-Ib. Numerical methods approximate A -I b by x j with residual b - Ax j in this subspace. A good basis for K j requires only multiplication by A at each step.
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lA-II = l/lAI and IATI = IAI.
The big formula for det(A) has a sum of n! terms, the cofactor formula uses determinants of size n - 1, volume of box = I det( A) I.
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Multiplication Ax
= Xl (column 1) + ... + xn(column n) = combination of columns.
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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.
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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).
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Polar decomposition A = Q H.
Orthogonal Q times positive (semi)definite H.
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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.
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Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.
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Saddle point of I(x}, ... ,xn ).
A point where the first derivatives of I are zero and the second derivative matrix (a2 II aXi ax j = Hessian matrix) is indefinite.
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Schur complement S, D - C A -} B.
Appears in block elimination on [~ g ].
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Similar matrices A and B.
Every B = M-I AM has the same eigenvalues as A.
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Toeplitz matrix.
Constant down each diagonal = time-invariant (shift-invariant) filter.
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Wavelets Wjk(t).
Stretch and shift the time axis to create Wjk(t) = woo(2j t - k).