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Textbooks / Math / Math Connects: Concepts, Skills, and Problem Solving Course 3 0

Math Connects: Concepts, Skills, and Problem Solving Course 3 0th Edition - Solutions by Chapter

Math Connects: Concepts, Skills, and Problem Solving Course 3 | 0th Edition | ISBN: 9780078740503 | Authors: Roger Day

Full solutions for Math Connects: Concepts, Skills, and Problem Solving Course 3 | 0th Edition

ISBN: 9780078740503

Math Connects: Concepts, Skills, and Problem Solving Course 3 | 0th Edition | ISBN: 9780078740503 | Authors: Roger Day

Math Connects: Concepts, Skills, and Problem Solving Course 3 | 0th Edition - Solutions by Chapter

Solutions by Chapter
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Since problems from 12 chapters in Math Connects: Concepts, Skills, and Problem Solving Course 3 have been answered, more than 1064 students have viewed full step-by-step answer. Math Connects: Concepts, Skills, and Problem Solving Course 3 was written by and is associated to the ISBN: 9780078740503. This expansive textbook survival guide covers the following chapters: 12. The full step-by-step solution to problem in Math Connects: Concepts, Skills, and Problem Solving Course 3 were answered by , our top Math solution expert on 11/23/17, 04:55AM. This textbook survival guide was created for the textbook: Math Connects: Concepts, Skills, and Problem Solving Course 3, edition: 0.

Key Math Terms and definitions covered in this textbook
  • Associative Law (AB)C = A(BC).

    Parentheses can be removed to leave ABC.

  • Cofactor Cij.

    Remove row i and column j; multiply the determinant by (-I)i + j •

  • Complex conjugate

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

  • Conjugate Gradient Method.

    A sequence of steps (end of Chapter 9) to solve positive definite Ax = b by minimizing !x T Ax - x Tb over growing Krylov subspaces.

  • Distributive Law

    A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

  • Exponential eAt = I + At + (At)2 12! + ...

    has derivative AeAt; eAt u(O) solves u' = Au.

  • Fibonacci numbers

    0,1,1,2,3,5, ... satisfy Fn = Fn-l + Fn- 2 = (A7 -A~)I()q -A2). Growth rate Al = (1 + .J5) 12 is the largest eigenvalue of the Fibonacci matrix [ } 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.

  • Hilbert matrix hilb(n).

    Entries HU = 1/(i + j -1) = Jd X i- 1 xj-1dx. Positive definite but extremely small Amin and large condition number: H is ill-conditioned.

  • Identity matrix I (or In).

    Diagonal entries = 1, off-diagonal entries = 0.

  • Markov matrix M.

    All mij > 0 and each column sum is 1. Largest eigenvalue A = 1. If mij > 0, the columns of Mk approach the steady state eigenvector M s = s > O.

  • 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.

  • Orthogonal matrix Q.

    Square matrix with orthonormal columns, so QT = Q-l. Preserves length and angles, IIQxll = IIxll and (QX)T(Qy) = xTy. AlllAI = 1, with orthogonal eigenvectors. Examples: Rotation, reflection, permutation.

  • Pivot.

    The diagonal entry (first nonzero) at the time when a row is used in elimination.

  • Plane (or hyperplane) in Rn.

    Vectors x with aT x = O. Plane is perpendicular to a =1= O.

  • Rayleigh quotient q (x) = X T Ax I x T x for symmetric A: Amin < q (x) < Amax.

    Those extremes are reached at the eigenvectors x for Amin(A) and Amax(A).

  • Solvable system Ax = b.

    The right side b is in the column space of A.

  • Symmetric matrix A.

    The transpose is AT = A, and aU = a ji. A-I is also symmetric.

  • Triangle inequality II u + v II < II u II + II v II.

    For matrix norms II A + B II < II A II + II B II·

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