Question: Let A and B be nonsingular n x n matrices. Show that cond(AB) cond(A)cond(B)

Let A and B be nonsingular n x n matrices. Show that
cond(AB) ≤ cond(A)cond(B)

Step by Step Solution

★★★★★

3.32 Rating (167 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

cond AB AB AB 1 A ... View full answer

blur-text-image
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)

Word file Icon

949-M-L-A-E (974).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

Let A and B be nonsingular n ( n matrices. Prove that AB and BA have the same eigenvalues?

Q:

Let A and B be nonempty, convex subsets in a normed linear space X with int A and int AB . Then A and B can be properly separated. Frequently stronger forms of separation are required. Two sets A and...

Q:

Let A and B be n n matrices with eigenvalues and , respectively. (a) Give an example to show that + need not be an eigenvalue of A + B. (b) Give an example to show that need not be an eigenvalue...

Q:

can you please help me with this Question 1 [2x3pts] a. Let A and B be nonsingular N x N matrices. Show that (AB)-1= B-IA-1. b. Let A and B be Nx N matrices; let C=AB. Starting from the definition of...

Q:

6. Let A and B be two n X n matrices. Show that a. (A + B) = At + Bt b. (AB = B At

Q:

(8 marks in total) (a) (4 marks) Let A and B be two n X n matrices such that A2 = 1, B2 = I and (AB) = I, where I is the nXn identity matrix. Prove that, in this case, AB = BA. (b) (4 marks) Give a...

Q:

14. Let A and B be two n x n matrices such that AB' = 0. Is B'A necessarily equal to zero? Show that tr (B'A) = 0.

Q:

Let A and B be arbitary n x n matrices. If B is invertible, prove that AB- = B 'A if and only if AB = BA

Q:

Let A and B be square, n X n matrices. (a) If A and B are both invertible is A + B necessarily invertible? Explain. (b) If the product AB is invertible does this imply that both A and Bare invertible

Q:

Let A and B denote invertible n x n matrices. (a) If A-1] = B], does it mean that A = P? Explain. (b) Show that A = B if and only if A-1B = I.

Q:

A microprocessor has a memory write timing as shown in Figure 3.19. Its manufacturer specifies that the width of the Write signal can be determined by T - 50, where T is the clock period in ns. a....

Q:

Visit www.alexa.com and search for Pandora.com to retrieve the websites analytics. Click on Get Details. a. What is Pandoras Alexa Traffic Rank, and what does that term mean? (Its above the graph.)...

Q:

Which one of the following risk premikumis compensaties for the inability to easily resell a bond prion formanumpy? Multiple Choice 0 0 : 2 9 : 1 2 Default risk Taxability Liquidity Inflation...

Q:

List, explain, and evaluate the major ideas of John Maynard Keynes, including the volatility of investment, sticky wages and prices, the macroeconomic problems created by wage and price deflation,...

Q:

Span {u, v} for all h and k. Let u= and v=12 Show that is in

Q:

In Exercises 1 and 2, mark each statement True or False. Justify each answer. 1. a Another notation for the vector b. The points in the plane corresponding to And Lie on a line through the origin. c....

Q:

Denote the columns of A by a1, a2, a3, and let W = Span {a1, a2, a3}. Let And a. Is b in {a1, a2, a3}? How many vectors are in {a1, a2, a3}? b. Is b in W? How many vectors are in W? c. Show that a1...

Q:

Please answer Question #39 and show work. A Treasury bill matures in 68 days and has a bond equivalent yield of 4.05 percent. What is the effective annual rate? A. 4.12 percent B. 4.14 percent C....

Q:

A pension fund manager is considering three mutual funds. The first is a stock fund, the second is a long-term bond fund, and the third is a money market fund that provides a safe return of 7%. The...

Q:

You ve observed the following returns on Crash - n - Burn Computer s stock over the past five years: 2 0 percent, 1 2 percent, 1 7 percent, 2 0 percent, and 1 0 percent. Suppose the average inflation...