×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide

Solutions for Chapter 8.1: Boolean Algebra Structure

Mathematical Structures for Computer Science | 7th Edition | ISBN: 9781429215107 | Authors: Judith L. Gersting

Full solutions for Mathematical Structures for Computer Science | 7th Edition

ISBN: 9781429215107

Mathematical Structures for Computer Science | 7th Edition | ISBN: 9781429215107 | Authors: Judith L. Gersting

Solutions for Chapter 8.1: Boolean Algebra Structure

Solutions for Chapter 8.1
4 5 0 359 Reviews
28
2
Textbook: Mathematical Structures for Computer Science
Edition: 7
Author: Judith L. Gersting
ISBN: 9781429215107

Chapter 8.1: Boolean Algebra Structure includes 30 full step-by-step solutions. This expansive textbook survival guide covers the following chapters and their solutions. Since 30 problems in chapter 8.1: Boolean Algebra Structure have been answered, more than 21202 students have viewed full step-by-step solutions from this chapter. This textbook survival guide was created for the textbook: Mathematical Structures for Computer Science, edition: 7. Mathematical Structures for Computer Science was written by and is associated to the ISBN: 9781429215107.

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

    Tv = Av + Vo = linear transformation plus shift.

  • Augmented matrix [A b].

    Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

  • Back substitution.

    Upper triangular systems are solved in reverse order Xn to Xl.

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

    The n roots are the eigenvalues of A.

  • Commuting matrices AB = BA.

    If diagonalizable, they share n eigenvectors.

  • 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).

  • Complex conjugate

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

  • Condition number

    cond(A) = c(A) = IIAIlIIA-III = amaxlamin. In Ax = b, the relative change Ilox III Ilx II is less than cond(A) times the relative change Ilob III lib II· Condition numbers measure the sensitivity of the output to change in the input.

  • Distributive Law

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

  • Identity matrix I (or In).

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

  • Iterative method.

    A sequence of steps intended to approach the desired solution.

  • Minimal polynomial of A.

    The lowest degree polynomial with meA) = zero matrix. This is peA) = det(A - AI) if no eigenvalues are repeated; always meA) divides peA).

  • Projection p = a(aTblaTa) onto the line through a.

    P = aaT laTa has rank l.

  • Reflection matrix (Householder) Q = I -2uuT.

    Unit vector u is reflected to Qu = -u. All x intheplanemirroruTx = o have Qx = x. Notice QT = Q-1 = Q.

  • Row picture of Ax = b.

    Each equation gives a plane in Rn; the planes intersect at x.

  • 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.

  • Solvable system Ax = b.

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

  • Special solutions to As = O.

    One free variable is Si = 1, other free variables = o.

  • Toeplitz matrix.

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

  • Trace of A

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

×
Log in to StudySoup
Get Full Access to Math - Textbook Survival Guide
Join StudySoup for FREE
Get Full Access to Math - Textbook Survival Guide
×
Reset your password