 23.5.23.1.78: Find a sh0l1est spanning tree by Prim's algorithm. Sketch it. For t...
 23.5.23.1.79: Find a sh0l1est spanning tree by Prim's algorithm. Sketch it. For t...
 23.5.23.1.80: Find a sh0l1est spanning tree by Prim's algorithm. Sketch it. For t...
 23.5.23.1.81: Find a sh0l1est spanning tree by Prim's algorithm. Sketch it.
 23.5.23.1.82: Find a sh0l1est spanning tree by Prim's algorithm. Sketch it.
 23.5.23.1.83: Find a sh0l1est spanning tree by Prim's algorithm. Sketch it.
 23.5.23.1.84: Find a sh0l1est spanning tree by Prim's algorithm. Sketch it.
 23.5.23.1.85: (Complexity) Show that Prim's algorithm has complexity 0(n2).
 23.5.23.1.86: How does Prim's algorithm prevent the formation of cycles as one gr...
 23.5.23.1.87: For a complete graph (or one that is almost complete), if our dara ...
 23.5.23.1.88: In what case will Prim's algorithm give S = E as the final result?
 23.5.23.1.89: TEAM PROJECT. Center of a Graph and Related Concepts. (a) Distance,...
 23.5.23.1.90: What would the result be if you applied Prim's algorithm to a graph...
 23.5.23.1.91: CAS PROBLEM. Prim's Algorithm. Write a program and apply it to Prob...
Solutions for Chapter 23.5: Shortest Spanning Trees. Prim's Algorithm
Full solutions for Advanced Engineering Mathematics  9th Edition
ISBN: 9780471488859
Solutions for Chapter 23.5: Shortest Spanning Trees. Prim's Algorithm
Get Full SolutionsThis expansive textbook survival guide covers the following chapters and their solutions. Since 14 problems in chapter 23.5: Shortest Spanning Trees. Prim's Algorithm have been answered, more than 43893 students have viewed full stepbystep solutions from this chapter. Chapter 23.5: Shortest Spanning Trees. Prim's Algorithm includes 14 full stepbystep solutions. Advanced Engineering Mathematics was written by and is associated to the ISBN: 9780471488859. This textbook survival guide was created for the textbook: Advanced Engineering Mathematics, edition: 9.

Basis for V.
Independent vectors VI, ... , v d whose linear combinations give each vector in V as v = CIVI + ... + CdVd. V has many bases, each basis gives unique c's. A vector space has many bases!

Cross product u xv in R3:
Vector perpendicular to u and v, length Ilullllvlll sin el = area of parallelogram, u x v = "determinant" of [i j k; UI U2 U3; VI V2 V3].

Dimension of vector space
dim(V) = number of vectors in any basis for V.

Elimination.
A sequence of row operations that reduces A to an upper triangular U or to the reduced form R = rref(A). Then A = LU with multipliers eO in L, or P A = L U with row exchanges in P, or E A = R with an invertible E.

Four Fundamental Subspaces C (A), N (A), C (AT), N (AT).
Use AT for complex A.

Free columns of A.
Columns without pivots; these are combinations of earlier columns.

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!).

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

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

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

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 equation AT Ax = ATb.
Gives the least squares solution to Ax = b if A has full rank n (independent columns). The equation says that (columns of A)·(b  Ax) = o.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

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.

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).

Row space C (AT) = all combinations of rows of A.
Column vectors by convention.

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

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·

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.