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Explorations in College Algebra 5th Edition - Solutions by Chapter

Explorations in College Algebra | 5th Edition | ISBN: 9780470466445 | Authors: Linda Almgren Kime

Full solutions for Explorations in College Algebra | 5th Edition

ISBN: 9780470466445

Explorations in College Algebra | 5th Edition | ISBN: 9780470466445 | Authors: Linda Almgren Kime

Explorations in College Algebra | 5th Edition - Solutions by Chapter

Explorations in College Algebra was written by Sieva Kozinsky and is associated to the ISBN: 9780470466445. This expansive textbook survival guide covers the following chapters: 9. This textbook survival guide was created for the textbook: Explorations in College Algebra, edition: 5. Since problems from 9 chapters in Explorations in College Algebra have been answered, more than 1555 students have viewed full step-by-step answer. The full step-by-step solution to problem in Explorations in College Algebra were answered by Sieva Kozinsky, our top Math solution expert on 12/23/17, 04:55PM.

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.

  • Companion matrix.

    Put CI, ... ,Cn in row n and put n - 1 ones just above the main diagonal. Then det(A - AI) = ±(CI + c2A + C3A 2 + .•. + cnA n-l - An).

  • Dimension of vector space

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

  • 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.

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

    Use AT for complex A.

  • Fourier matrix F.

    Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

  • Hermitian matrix A H = AT = A.

    Complex analog a j i = aU of a symmetric matrix.

  • Independent vectors VI, .. " vk.

    No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

  • Length II x II.

    Square root of x T x (Pythagoras in n dimensions).

  • Linear combination cv + d w or L C jV j.

    Vector addition and scalar multiplication.

  • Linearly dependent VI, ... , Vn.

    A combination other than all Ci = 0 gives L Ci Vi = O.

  • Multiplication Ax

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

  • 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 •

  • Outer product uv T

    = column times row = rank one matrix.

  • Partial pivoting.

    In each column, choose the largest available pivot to control roundoff; all multipliers have leij I < 1. See condition number.

  • Particular solution x p.

    Any solution to Ax = b; often x p has free variables = o.

  • 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.

  • Spectrum of A = the set of eigenvalues {A I, ... , An}.

    Spectral radius = max of IAi I.

  • Toeplitz matrix.

    Constant down each diagonal = time-invariant (shift-invariant) filter.

  • Wavelets Wjk(t).

    Stretch and shift the time axis to create Wjk(t) = woo(2j t - k).

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