Access Others Questions and Answers | CFS

Recent Others Questions & Answers

Let A ? Mn be doubly stochastic. (a) Show that A cannot have exactly n + 1 positive entries. (b) If A is not a permutation matrix, explain why it has ...

Let A ? Mn be doubly stochastic. (a) Show that A cannot have exactly n + 1 positive entries. (b) If A is not a permutation matrix, explain why it has at most n2 ? n ? 2 zero entries....

View Answer

Explain why a matrix is an extreme point of the compact convex set of doubly stochastic n-by-n matrices if and only if it is a permutation matrix....

Explain why a matrix is an extreme point of the compact convex set of doubly stochastic n-by-n matrices if and only if it is a permutation matrix....

View Answer

Show that any permutation matrix is an extreme point of the convex set of doubly stochastic matrices. What more can you say if A is a permutation matr...

Show that any permutation matrix is an extreme point of the convex set of doubly stochastic matrices. What more can you say if A is a permutation matrix?...

View Answer

Let | ...

Let | ...

View Answer

Let A ? Mn be doubly stochastic and let ? 1(A) be its largest singular value. Show in two ways that ? 1(A) = ?(A) = 1, that is, a doubly stochastic ma...

Let A ? Mn be doubly stochastic and let ? 1(A) be its largest singular value. Show in two ways that ? 1(A) = ?(A) = 1, that is, a doubly stochastic matrix is a spectral matrix. (a) Use the representation (8.7.3). (b) Use (2.6.P29)....

View Answer

Let A ? Mn be a nonnegative nonzero matrix that has a positive eigenvector. Explain why every maximum-modulus eigenvalue of A is semisimple....

Let A ? Mn be a nonnegative nonzero matrix that has a positive eigenvector. Explain why every maximum-modulus eigenvalue of A is semisimple....

View Answer

Let A ? Mn be a nonnegative nonzero matrix that has a positive eigenvector x = [xi], and let D = diag(x1, . . . , xn). Show that ?(A)?1D?1 AD is stoch...

Let A ? Mn be a nonnegative nonzero matrix that has a positive eigenvector x = [xi], and let D = diag(x1, . . . , xn). Show that ?(A)?1D?1 AD is stochastic. This observation permits many questions about nonnegative matrices with a positive eigenvector to be reduced to questions about stochastic matr...

View Answer

Show that the sets of stochastic and doubly stochastic matrices in Mn each constitute a semigroup under matrix multiplication; that is, if A, B ? Mn a...

Show that the sets of stochastic and doubly stochastic matrices in Mn each constitute a semigroup under matrix multiplication; that is, if A, B ? Mn are (doubly) stochastic, then AB is (doubly) stochastic....

View Answer

Show that the sets of stochastic and doubly stochastic matrices in Mn each constitute a semigroup under matrix multiplication; that is, if A, B ? Mn a...

Show that the sets of stochastic and doubly stochastic matrices in Mn each constitute a semigroup under matrix multiplication; that is, if A, B ? Mn are (doubly) stochastic, then AB is (doubly) stochastic....

View Answer

Suppose that A ? Mn is irreducible and nonnegative, let n ? 2, and write Am = [aij (m)] for m = 1, 2, . . . . For each pair i, j, show that aij (m) > ...

Suppose that A ? Mn is irreducible and nonnegative, let n ? 2, and write Am = [aij (m)] for m = 1, 2, . . . . For each pair i, j, show that aij (m) > 0 for infinitely many values of m. Give an example to show that there may also be infinitely many values of m for which a (m) ij = 0....

View Answer

textbook solutions

Just $7.00/month

Subscription

Get immediate access to 24/7 Homework Help, step-by-step solutions, instant homework answer to over 40 million Textbook solution and Q/A

Pay $7.00/month for Better Grades

support@crazyforstudy.com

+1-775-500-0051