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Textbooks / Math / Elementary Linear Algebra, Binder Ready Version: Applications Version 11

Elementary Linear Algebra, Binder Ready Version: Applications Version 11th Edition - Solutions by Chapter

Full solutions for Elementary Linear Algebra, Binder Ready Version: Applications Version | 11th Edition

ISBN: 9781118474228

Elementary Linear Algebra, Binder Ready Version: Applications Version | 11th Edition - Solutions by Chapter

Solutions by Chapter
4 5 0 330 Reviews
Textbook: Elementary Linear Algebra, Binder Ready Version: Applications Version
Edition: 11
Author: Howard Anton, Chris Rorres
ISBN: 9781118474228

This textbook survival guide was created for the textbook: Elementary Linear Algebra, Binder Ready Version: Applications Version, edition: 11. The full step-by-step solution to problem in Elementary Linear Algebra, Binder Ready Version: Applications Version were answered by , our top Math solution expert on 03/14/18, 04:26PM. Since problems from 80 chapters in Elementary Linear Algebra, Binder Ready Version: Applications Version have been answered, more than 25875 students have viewed full step-by-step answer. This expansive textbook survival guide covers the following chapters: 80. Elementary Linear Algebra, Binder Ready Version: Applications Version was written by and is associated to the ISBN: 9781118474228.

Key Math Terms and definitions covered in this textbook
  • Block matrix.

    A matrix can be partitioned into matrix blocks, by cuts between rows and/or between columns. Block multiplication ofAB is allowed if the block shapes permit.

  • Cholesky factorization

    A = CTC = (L.J]))(L.J]))T for positive definite A.

  • Dimension of vector space

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

  • Fast Fourier Transform (FFT).

    A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn-1c can be computed with ne/2 multiplications. Revolutionary.

  • Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).

    Use AT for complex A.

  • Full row rank r = m.

    Independent rows, at least one solution to Ax = b, column space is all of Rm. Full rank means full column rank or full row rank.

  • Gauss-Jordan method.

    Invert A by row operations on [A I] to reach [I A-I].

  • Gram-Schmidt orthogonalization A = QR.

    Independent columns in A, orthonormal columns in Q. Each column q j of Q is a combination of the first j columns of A (and conversely, so R is upper triangular). Convention: diag(R) > o.

  • Least squares solution X.

    The vector x that minimizes the error lie 112 solves AT Ax = ATb. Then e = b - Ax is orthogonal to all columns of A.

  • Left nullspace N (AT).

    Nullspace of AT = "left nullspace" of A because y T A = OT.

  • Linear transformation T.

    Each vector V in the input space transforms to T (v) in the output space, and linearity requires T(cv + dw) = c T(v) + d T(w). Examples: Matrix multiplication A v, differentiation and integration in function space.

  • Norm

    IIA II. The ".e 2 norm" of A is the maximum ratio II Ax II/l1x II = O"max· Then II Ax II < IIAllllxll and IIABII < IIAIIIIBII and IIA + BII < IIAII + IIBII. Frobenius norm IIAII} = L La~. The.e 1 and.e oo norms are largest column and row sums of laij I.

  • 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.

  • Orthonormal vectors q 1 , ... , q n·

    Dot products are q T q j = 0 if i =1= j and q T q i = 1. The matrix Q with these orthonormal columns has Q T Q = I. If m = n then Q T = Q -1 and q 1 ' ... , q n is an orthonormal basis for Rn : every v = L (v T q j )q j •

  • Permutation matrix P.

    There are n! orders of 1, ... , n. The n! P 's have the rows of I in those orders. P A puts the rows of A in the same order. P is even or odd (det P = 1 or -1) based on the number of row exchanges to reach I.

  • Pseudoinverse A+ (Moore-Penrose inverse).

    The n by m matrix that "inverts" A from column space back to row space, with N(A+) = N(AT). A+ A and AA+ are the projection matrices onto the row space and column space. Rank(A +) = rank(A).

  • Schur complement S, D - C A -} B.

    Appears in block elimination on [~ g ].

  • Symmetric factorizations A = LDLT and A = QAQT.

    Signs in A = signs in D.

  • Trace of A

    = sum of diagonal entries = sum of eigenvalues of A. Tr AB = Tr BA.