Prove that the condition number of a nonsingular matrix is given by k(A) = ||A||2 ||A-1||2.

Question:

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

Step by Step Answer:

Related Book For book-img-for-question

Applied Linear Algebra

ISBN: 978-0131473829

1st edition

Authors: Peter J. Olver, Cheri Shakiban

See More Books

Question Posted: Jun 18, 2016 08:58 AM

See More Questions

Let A and B be n n matrices. Prove that if AB = I then BA = I. What is the significance of this result in terms of the definition of a nonsingular matrix?
Show that if A is an n n nonsingular matrix with singular values s1, s2, ..., sn, then the l2 condition number of A is K2 (A) = (s1 / sn).
Use the result in Exercise 15 to determine the condition numbers of the nonsingular square matrices in Exercises 1 and 2. In exercise Show that if A is an n n nonsingular matrix with singular values...
Discuss what you see as the role of ethics as it pertains to management and managers. Does management, in your view, help shape the values and ethics of an organization? What about an organization's...
What types of businesses are most likely to attract venture capital? What investment criteria do venture capitalists use when screening potential businesses? How do these compare to the typical...
What is the difference between a stocks price and its intrinsic value? AppendixLO1
What is the difference between a value and price-weighted index? Explain.
The trial balance of Neal Company as of January 31, 2019, after the company completed the first month of operations, is shown in the partial worksheet below. INSTRUCTIONS 1. Record the trial balance...
JCW, a Private Equity firm, is interested in tendering 100% of JZ Inc's stock for $40 per share. In addition of purchasing all of the 10 milion JZ Inc. outstanding shares, JCW is planning to...
A client uses TCP to send data to a server. The data consist of 16 bytes. Calculate the efficiency of this transmission at the TCP level (ratio of useful bytes to total bytes).
True or false: If B = S-1AS are similar matrices, then (a) ||B|| = ||A|| (b) ||B||2 = ||A||2 (c) p(B) = p(A)
(i) Find an explicit formula for the 1 matrix norm ||A|||1. (ii) Compute the 1 matrix norm of the matrices in Exercise 10.3.1, and discuss convergence.
Three friends organized Rapid City Roller Rink on October 1, 2010. The following transactions occurred during the first month of operations: October 1: Received contribution of $22,000 from each of...
Let two planes be given by 2x-y+z = 8 and z = x+y-5 (a) Find the angle between the two planes. Leave your answer in degrees and round to the nearest tenth. (b) Find the vector equation of the line of...
9-2. The profile of a gear tooth shown in Fig. P9.2 is approximated by the trigonometric equation y(x) = a. Estimate the area A using eight rectangles of equal width A x = 1/8, b. Calculate the exact...
tube is hinged to a rotating base as shown in Fig. 4. At the instant shown, the base rotates about the z axis with a constant angular velocity ! 1 = 2 rad/s. At the same instant, the 2 tube rotates...
Find the limit analytically. -7x2+5x-10 lim 0 9x+13x+11 Find the limit analytically. lim +80 4x-13 5x+6x-11
Write a recursive function for the running time T(n) of the function given below. Prove using the iterative method that T(n) = (n). function( int n) { if(n=1) return; for(int i = 1; i
The photoelectric effect can be used in engineering designs for practical applications. For example, infrared goggles used in night-vision applications have materials that give an electrical signal...
(8%) Problem 6: A student attaches a f= 3.5 kHz oscillator to one end of a metal rail of length L = 25 m. The student turns on the oscillator and uses a piezoelectric gauge at the other end to...
A lighthouse is located on a small island 3 km away from the nearest point P on a straight shoreline and its light makes four revolutions per minute. How fast is the beam of light moving along the...
A plane flying with a constant speed of 300 km/h passes over a ground radar station at an altitude of 1 km and climbs at an angle of 30o. At what rate is the distance from the plane to the radar...
Two people start from the same point. One walks east at 3 mi/h and the other walks northeast at 2 mi/h. How fast is the distance between the people changing after 15 minutes?
What is the risk profile of your company? (How much overall risk is there in this firm? Where is this risk coming from (market, firm, industry or currency)? (APPLE COMPANY LATEST DATA) How is the...
What is the duration for the following bond with annual payments? 5.6300 5.7957 4.9894 5.1910 5.3806
DOLLAR TREE GROCERY OUTLET Short-Term Liquidity 2021 2022 2021 2022 Current Ratio 1.35 1.51 1.86 1.67 Quick Ratio 0.24 0.15 0.63 0.42 Cash Ratio Cash Conversion Cycle 34.78 45.75 19.41 21.61 Days...

Prove that the condition number of a nonsingular matrix is given by k(A) = ||A||2 ||A-1||2.

Question:

Step by Step Answer:

By definition k A 1 n Now A 2 1 On the ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions