 1.6.1: According to the assignment rule, what is the precondition in the f...
 1.6.2: According to the assignment rule, what is the precondition in the f...
 1.6.3: According to the assignment rule, what is the precondition in the f...
 1.6.4: According to the assignment rule, what is the precondition in the f...
 1.6.5: Verify the correctness of the following program segment with the pr...
 1.6.6: Verify the correctness of the following program segment with the pr...
 1.6.7: Verify the correctness of the following program segment with the pr...
 1.6.8: Verify the correctness of the following program segment with the pr...
 1.6.9: Verify the correctness of the following program segment to compute ...
 1.6.10: Verify the correctness of the following program segment to compute ...
 1.6.11: Verify the correctness of the following program segment with the pr...
 1.6.12: Verify the correctness of the following program segment with the pr...
 1.6.13: Verify the correctness of the following program segment with the pr...
 1.6.14: Verify the correctness of the following program segment to compute ...
 1.6.15: Verify the correctness of the following program segment to compute ...
 1.6.16: Verify the correctness of the following program segment with the as...
Solutions for Chapter 1.6: Logic Programming
Full solutions for Mathematical Structures for Computer Science  7th Edition
ISBN: 9781429215107
Solutions for Chapter 1.6: Logic Programming
Get Full SolutionsSince 16 problems in chapter 1.6: Logic Programming have been answered, more than 20070 students have viewed full stepbystep solutions from this chapter. Mathematical Structures for Computer Science was written by and is associated to the ISBN: 9781429215107. Chapter 1.6: Logic Programming includes 16 full stepbystep solutions. This expansive textbook survival guide covers the following chapters and their solutions. This textbook survival guide was created for the textbook: Mathematical Structures for Computer Science, edition: 7.

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

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.

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

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

Full column rank r = n.
Independent columns, N(A) = {O}, no free variables.

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.

Kronecker product (tensor product) A ® B.
Blocks aij B, eigenvalues Ap(A)Aq(B).

Linear combination cv + d w or L C jV j.
Vector addition and scalar multiplication.

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.

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).

Normal matrix.
If N NT = NT N, then N has orthonormal (complex) eigenvectors.

Pseudoinverse A+ (MoorePenrose 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).

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.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Singular matrix A.
A square matrix that has no inverse: det(A) = o.

Skewsymmetric matrix K.
The transpose is K, since Kij = Kji. Eigenvalues are pure imaginary, eigenvectors are orthogonal, eKt is an orthogonal matrix.

Spanning set.
Combinations of VI, ... ,Vm fill the space. The columns of A span C (A)!

Stiffness matrix
If x gives the movements of the nodes, K x gives the internal forces. K = ATe A where C has spring constants from Hooke's Law and Ax = stretching.

Transpose matrix AT.
Entries AL = Ajj. AT is n by In, AT A is square, symmetric, positive semidefinite. The transposes of AB and AI are BT AT and (AT)I.

Unitary matrix UH = U T = UI.
Orthonormal columns (complex analog of Q).