Question: Show that A+ is the only matrix that satisfies the Penrose conditions for A. To do this, assume that A' is a matrix satisfying the

Show that A+ is the only matrix that satisfies the Penrose conditions for A. To do this, assume that A' is a matrix satisfying the Penrose conditions: (a) AA'A = A, (b) A'AA ' = A', and (c) AA' and A' A are symmetric. Prove that A' = A+.

Step by Step Solution

★★★★★

3.50 Rating (170 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

As suggested in the hint suppose that A0 is a matrix satisfying t... View full answer

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Document Format (1 attachment)

859-L-A-L-S (2909).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Show that if A is a square matrix that satisfies the equation A2 - 2A+I=0, then A-1=2I - A.

Let A = XYT, where X is an m r matrix, YT is an r n matrix, and XTX and YTY are both nonsingular. Show that the matrix B = Y (YTY)-1(XTX)-1 XT satisfies the Penrose conditions and hence must equal...

Show that (A + ) + = A. [Show that A satisfies the Penrose conditions for A + . By Exercise 52, A must therefore be (A + ) + .]

y' = ky , to = 0, k has n linearly independent eigenvector insing notation of Section 7.7 in the text D. using a careful proof in a couple of steps to show that P ( t) = I (t) T 10) , and then show...

Submitted to Management Science manuscript MS-0001-1922.65 Authors are encouraged to submit new papers to INFORMS journals by means of a style file template, which includes the journal title....

I'm stuck in the question solve this question quickly 2. [Pseudo-inverse and QR. ] The pseudo inverse Z of a matrix A ( RX , m > n is (uniquely) defined through the following conditions (called...

Please provide detailed solution with explanation and justification asap to get a upvote 2. [Pseudo-inverse and QR, The pseudo inverse Z of a matrix A E Rmxa, m > n is (uniquely) defined through the...

Please help me solve the following 8 questions so that I can compare it with my answers Throughout this module, we have assumed that SSE/o' ~ Xn-p; however, we have never seen a proof for it! We now...

HW 12, MAT 312/AMS 351: SPRING 2017 Problem 1. (1) Set H = {4a + 6b | a, b Z} Z. Show that H is a subgroup of Z. (2) Is H cyclic? Problem 2. Write down all the cyclic subgroups of the following...

Briefly describe ASCII and Unicode and draw attention to any relationship between them. [3 marks] (b) Briefly explain what a Reader is in the context of reading characters from data. [3 marks] A...

Wonderland Preschool operates a not-for-profit morning preschool. Each family pays a nonrefundable registration fee of $105 per child per school year Monthly tuition for the nine-month school year...

A double-acting reciprocating pump, running at 100 RPM delivers 0.03 m^3 /sec of water. The diameter of the piston and the stroke length is 15 cm and 600 mm, respectively. Further, the diameter of...

2 What do you think about Councillor Andersons remarks about protecting jobs?

What Is the Retail Price? Suppose a buyer wanted to buy goods that cost $300 and the customary markup on retail was 20 percent. Demonstrate two methods that could be used to calculate the retail...

The Gemmers decide to give their children a weekly allowance that is directly proportional to each child's age. Their 6-year-old daughter receives an allowance of $4.50. What is their 11-year-old...

The weight W that a horizontal beam can support varies inversely as the length L of the beam. Suppose an 8-m beam can support 1200 kg. How many kilograms can a 14-m beam support? W

The time t required to drive a fixed distance varies inversely as the speed r. It takes 5 hr at a speed of 80 km/h to drive a fixed distance. How long will it take to drive the same distance at a...

Carter Corporation's sales are expected to increase from $5 million in 2012 to $6 million in 2015, or by 20%. Its assets totaled $2 million at the end of 2014. Carter is at full capacity, so its...

A Japanese exporter has a 61,000,000 receivable due in one year. Detail a strategy using a money market hedge that will eliminate any exchange rate risk. 1-year rates of interest Spot exchange rates...

Investment A pays 8% simple interest for 10 years Investment B pays 7.75% compound interest for 10 years. Both require an initial $10,000 investment. The future value of A minus the future value of B...