×
Log in to StudySoup
Get Full Access to
Join StudySoup for FREE
Get Full Access to

Already have an account? Login here
×
Reset your password

Textbooks / Math / Loose-leaf Version for For All Practical Purposes 10

Loose-leaf Version for For All Practical Purposes 10th Edition Solutions

Do I need to buy Loose-leaf Version for For All Practical Purposes | 10th Edition to pass the class?

ISBN: 9781464124839

Loose-leaf Version for For All Practical Purposes | 10th Edition - Solutions by Chapter

Do I need to buy this book?
1 Review

72% of students who have bought this book said that they did not need the hard copy to pass the class. Were they right? Add what you think:

Loose-leaf Version for For All Practical Purposes 10th Edition Student Assesment

Shayne from Pennsylvania State University said

"If I knew then what I knew now I would not have bought the book. It was over priced and My professor only used it a few times."

Textbook: Loose-leaf Version for For All Practical Purposes
Edition: 10
Author: COMAP
ISBN: 9781464124839

The full step-by-step solution to problem in Loose-leaf Version for For All Practical Purposes were answered by , our top Math solution expert on 10/03/18, 03:08PM. This expansive textbook survival guide covers the following chapters: 0. Loose-leaf Version for For All Practical Purposes was written by and is associated to the ISBN: 9781464124839. Since problems from 0 chapters in Loose-leaf Version for For All Practical Purposes have been answered, more than 200 students have viewed full step-by-step answer. This textbook survival guide was created for the textbook: Loose-leaf Version for For All Practical Purposes, edition: 10.

Key Math Terms and definitions covered in this textbook
  • Affine transformation

    Tv = Av + Vo = linear transformation plus shift.

  • Characteristic equation det(A - AI) = O.

    The n roots are the eigenvalues of A.

  • 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.

  • 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.

  • Dot product = Inner product x T y = XI Y 1 + ... + Xn Yn.

    Complex dot product is x T Y . Perpendicular vectors have x T y = O. (AB)ij = (row i of A)T(column j of B).

  • Elimination matrix = Elementary matrix Eij.

    The identity matrix with an extra -eij in the i, j entry (i #- j). Then Eij A subtracts eij times row j of A from row i.

  • 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.

  • 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.

  • Indefinite matrix.

    A symmetric matrix with eigenvalues of both signs (+ and - ).

  • Inverse matrix A-I.

    Square matrix with A-I A = I and AA-l = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B-1 A-I and (A-I)T. Cofactor formula (A-l)ij = Cji! detA.

  • Iterative method.

    A sequence of steps intended to approach the desired solution.

  • 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.

  • Length II x II.

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

  • 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.

  • 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.

  • Rank one matrix A = uvT f=. O.

    Column and row spaces = lines cu and cv.

  • 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.

  • Symmetric matrix A.

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