If P is an n 1 matrix such that PT P = 1, then H =

Question:

If P is an n × 1 matrix such that PT P = 1, then H = I - 2PPT is called the corresponding Householder matrix (named after the American mathematician A. S. Householder).
Prove that if H is any Householder matrix, then H = HT and HTH = I.

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

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0471669593

9th edition

Authors: Howard Anton, Chris Rorres

See More Books

Question Posted: Jun 17, 2016 07:58 AM

See More Questions

Let W be an n 1 matrix such that WT W = 1. The n n matrix H = In - 2WWT is called a Householder* matrix. (a) Show that H is symmetric. (b) Show that H-1 = HT.
The idea is that elementary operations can be accomplished by matrix multiplication. If A is an m x n matrix on which we want to do an elementary operation, then there is a matrix E such that EA is...
Let {S1, S2, . . . , Sn} be a collection of nonempty compact subsets of an m-dimensional linear space, and let x conv We consider the Cartesian product of the convex hulls of Si, namely Every point...
On August 31, 2014, Nina Herrera borrowed $5,000 from Second State Bank. Herrera signed a note payable, promising to pay the bank principal plus interest on August 31, 2015. The interest rate on the...
The manager of Moores Catalog Showroom is trying to predict how much revenue will be generated by each major department in the store during 2006. The manager has estimated the minimum and maximum...
The most recent financial statements for Williamson, Inc., are shown here (assuming no income taxes): Assets and costs are proportional to sales; debt and equity are not. No dividends are paid. Next...
If a nurse disagrees with a physicians written orders, discuss what action the nurse should take to protect the patients safety.
Complete the following statements by filling in the blanks. (a) In a period in which a taxable temporary difference reverses, the reversal will cause taxable income to be ___________ (less...
Using this information listed on the table please help me findTotal debits or credits from the unadjusted trial balanceTotal debits or credits from the adjusted trial balanceTotal revenue which is 2...
According to the U.S. Census, roughly half of all marriages in the United States end in divorce. Researchers from leading universities have shown that the emotions aroused by one persons divorce can...
Use part (c) of Exercise 24 to show that State all the assumptions you make in obtaining this formula. dA- - A-1dA A -1 dz dx
Use the result in part (a) to find An if 00c 0b0 a01
In an Idaho Potato Commission survey of 1000 adults, subjects are asked to select their favorite vegetables, and responses of potatoes, corn, broccoli, tomatoes, or other were recorded. Determine...
What are the pros and cons of the Autocratic Leader and the Collegial Leader in terms of disaster management?
Explain how judges bargain and negotiate on collegial courts.?
Human relations, teamwork and leadership. How is you relation to your staff, to others and collegial relations: physician and administrator.? Discuss
Marshall was nearing retirement age and was concerned about his retirement savings. He thought the stock market was too risky, so he put his money into a certificate of deposit (CD) at his local...
Insurance is protection against possible financial loss. All types of insurance have one similarity as it will provide you with peace of mind that comes to be your survivors, pay medical expenses,...
For Problem find x, y, or b without using a calculator. log b 64 = 3
When the Department of Homeland Security created a color-coded system to prepare government officials and the public against terrorist attacks, what did it do right and what did it do wrong?
Let V be an inner product space. Show that if v is orthogonal to w1, w2....wk, then v is orthogonal to every vector in span {w1, w2..... wk}.
Suppose that {v1, v2.... vn} is an orthonormal set in Rn with the standard inner product. Let the matrix A be given by A = [v1 v2 vn]. Show that A is non-singular and compute its inverse. Give...
If A is nonsingular, prove that ATA is positive definite.
"Managing Away Bad Habits Team Assignment Organizational Behavior IILeadership Assigned is ashort case from the exercise Managing Away Bad Habits. The task is to develop a turnaround strategy for...
"Managing Away Bad Habits Team Assignment Organizational Behavior IILeadership Assigned is ashort case from the exercise Managing Away Bad Habits. The task is to develop a turnaround strategy for...
11 The APRN unit director is working at an agency that has a high incidence of medication errors, specifically with heparin. One recent error had a patient receive twice the prescribed dose. Which...

If P is an n 1 matrix such that PT P = 1, then H =

Question:

Step by Step Answer:

If P is an n 1 matrix such that P T P 1 then H I 2PP T ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions