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# Solutions for Chapter 6.3: Decision Trees

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

ISBN: 9781429215107

Solutions for Chapter 6.3: Decision Trees

Solutions for Chapter 6.3
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##### ISBN: 9781429215107

Mathematical Structures for Computer Science was written by Patricia and is associated to the ISBN: 9781429215107. Chapter 6.3: Decision Trees includes 23 full step-by-step solutions. Since 23 problems in chapter 6.3: Decision Trees have been answered, more than 4433 students have viewed full step-by-step solutions from this chapter. 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.

Key Math Terms and definitions covered in this textbook
• Back substitution.

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

• Column space C (A) =

space of all combinations of the columns of A.

• Diagonalizable matrix A.

Must have n independent eigenvectors (in the columns of S; automatic with n different eigenvalues). Then S-I AS = A = eigenvalue matrix.

• 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.

• Free variable Xi.

Column i has no pivot in elimination. We can give the n - r free variables any values, then Ax = b determines the r pivot variables (if solvable!).

• Full column rank r = n.

Independent columns, N(A) = {O}, no free variables.

• Hessenberg matrix H.

Triangular matrix with one extra nonzero adjacent diagonal.

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

• 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).

• Nullspace matrix N.

The columns of N are the n - r special solutions to As = O.

• 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.

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

P = aaT laTa has rank l.

• Pseudoinverse A+ (Moore-Penrose 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).

• Row picture of Ax = b.

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

• Row space C (AT) = all combinations of rows of A.

Column vectors by convention.

• Singular matrix A.

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

• Solvable system Ax = b.

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

• Spanning set.

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

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