Show that a permutation matrix with m inversions can be row swapped to the identity in m

Question:

Show that a permutation matrix with m inversions can be row swapped to the identity in m steps. Contrast this with Corollary 4.5.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Linear Algebra

ISBN: 9780982406212

1st Edition

Authors: Jim Hefferon

See More Books

Question Posted: Jun 01, 2016 02:13 AM

See More Questions

Suppose A = PtLU, where P is a permutation matrix, L is a lower-triangular matrix with ones on the diagonal, and U is an upper-triangular matrix. a. Count the number of operations needed to compute...
Find a permutation matrix P and an LU-factorization of PA if A is: (a) (b) 2001[1 1 0-1 -2 1 21000 0 2 00 01-1 01 1-1000 1-2-1 -1 12 00 0 1 301-1J10 000 -6
This exercise outlines a proof of the Birkhoff-von Neumann Theorem. (a) For n Z+, an n n matrix is called a permutation matrix if there is exactly one 1 in each row and column, and all other...
A set of 2M biorthogonal signals is obtained from a set of M orthogonal signals by augmenting it with the negative of each signal in the set. (a) The extension of orthogonal to biorthogonal signals...
Suppose that the government reduces spending on highway construction by $10 billion. Which way does the aggregate-demand curve shift? Explain why the shift might be larger than $10 billion. Explain...
Betty Blacks investment club wants to buy the stock of either NewSoft Inc. or Capital Corp. In this connection, Black has prepared the following table. You have been asked to help her interpret the...
Which of the following statements about the architecture of a neural network is false? a. The output layer of a neural network for a regression task commonly consists of only one neuron. b. The...
Using the descriptions of the attributes given in the figure, convert the ERD shown in Figure into a dependency diagram that is in at least 3NF.
A positive charge q = 2.60 C on a frictionless horizontal surface is attached to a spring of force constant k as in the figure shown below. When a charge of 42 = -8.350 C is placed 9.50 cm away from...
About 40 people will lose their jobs when Burton closes its Burlington factory, and the company is working with the state of Vermont to provide them with help in finding new employment. How do you...
Prove that the matrix of the permutation inverse is the transpose of the matrix of the permutation P-1 = PT, for any permutation .
For any permutation Ï let g(Ï) be the integer defined in this way. (This is the product, over all indices i and j with i (a) Compute the value of g on all 2-permutations. (b) Compute the...
This tale of a sort of sting operation required participation from business, government, and a professional. John Nicolo was a real property appraiser who did appraisal work for Eastman Kodak, Inc....
Write ME if the given is a plain mathematical expression and write MS if it is a mathematical sentence. (1 point each) 1. x + y 5 2. [a, b] 1. 2. 3. 4. 5. 3. V = rh + 4. MMXX 5.32 Z such that 22 16...
You are an employee of the human resources division of a major Canadian company. You have been assigned the task of designing a workplace policy (the business does not currently have a policy) that...
3. Marie was employed by Rigney Construction as a bookkeeper and office manager for over 10 years. Without notice or explanation, Rigney informed Marie that her services were no longer required and...
Ali offered to purchase Sams pool for $400 cash. Ali and sam agreed that sam would deliver the pool to Alis house on march 1, at which time Ali would pay the $400. On march 1, when sam did not...
Buyer, who has never owned a computer, goes to Merchant Seller and buys a used computer for $4,000. Buyer is not pressured to purchase this computer, but Buyer does no research and does not price...
The following are the statements of financial position of A. Brooks as at 30 June 20X0 and 30 June 20X1: Additional information 1. There were no disposals of non-current assets during the year. 2....
Assume Eq. 6-14 gives the drag force on a pilot plus ejection seat just after they are ejected from a plane traveling horizontally at 1300 km/h. Assume also that the mass of the seat is equal to the...
Let V be a vector space and let x V. Show that: (a) 0 = 0 for each scalar . (b) If x = 0, then either = 0 or x = 0.
Given (a) Is x Span(x1, x2)? (b) Is y Span(x1, x2)? Prove your answers. 925 123
Let {x1, x2,..., xk} be a spanning set for a vector space V. (a) If we add an additional vector xk+1 to the set, will we still have a spanning set? Explain. (b) If we delete one of the vectors, say...
Mary was so excited about the holiday shopping season that she could hardly wait for the Black Friday sales. She got up early and spent all day at her favorite store, Mega Deals, shopping. Mary was...
This can be done as a group or individually. If done in a group, all group members must submit a copy of this assignment to receive a grade. If you were to open a business, what type of business...
6.(5pts) A total charge Q is distributed uniformly over a ring of radius R. We found an expression for the value of the electric field on the axis of the ring, E(x), a distance x from the center of...

Show that a permutation matrix with m inversions can be row swapped to the identity in m

Question:

Step by Step Answer:

This does not say that m is the least number of swaps to produce an identity nor does it say tha...View the full answer

Linear Algebra

Students also viewed these Linear Algebra questions