Explain why ||A|| = max|aij| defines a norm on the space of n x n matrices. Show

Question:

Explain why ||A|| = max|aij| defines a norm on the space of n x n matrices. Show by example that this is not a matrix norm, i.e., (10.33) is not necessarily valid.

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 08:59 AM

See More Questions

Prove directly from the axioms of Definition 3.12 that (10.40) defines a norm on the space of n n matrices.
Prove that || || defines a norm on the vectors space V. V = C[0, 1], ||f|| = F(x)|dx
Prove that defines a norm on the vectors space V. max |f(x)| 0
Decedent died owning an insurance policy that would pay $2 million to Beneficiary. Six months later, the insurance company paid Beneficiary $2 million plus $50,000 interest. What portion of the...
Why is it so difficult for most small business owners to raise the capital needed to start, operate, or expand their ventures?
Compare strategy formulation with strategy implementation in terms of each being an art or a science.
Tabletop Snow Zone is a ski field on the outskirts of Perth. It offers ski packages for the both experienced and novice skiers and also operates a caf and gear shop on the mountain. Tabletop Snow...
The King Corporation has total annual revenue of $800,000; expenses other than depreciation of $350,000; depreciation expense of $200,000 for tax purposes; and depreciation expense of $130,000 for...
Total fixed costs are $32,200 for Cullumber Inc. It has a unit contribution margin of $19 and a contribution margin ratio of 35%. Compute the break-even point in sales dollars. Break-even point in...
Richard chooses technique 0 and 2 requiring 10+10-20 efforts and provising 10+11=21 benefits. Hence, 21 is returned as the output Example 2: input1: 3 input2: (10,10,10,10) input3: (10,11,12,15)...
Let A be an n n matrix with singular value vector = (1,... , 1). Prove that (a) |||| = ||A||2; (b) ||||2 = ||A||F, the Frobenius norm of Exercise 10.3.16. Remark: ||||2 (also defines a useful...
Prove that the closed curve parametrized in (10.37) is an ellipse. What are its semi-axes?
Two balls are drawn in succession, without replacement, from a box containing 3 blue and 2 white balls (Fig. 4). What is the probability of drawing a white ball on the second draw? Figure 4
How can marketing managers apply the DATA process to evaluate social media marketing efforts?
What are the differences between sukuk and bonds?
What are the steps in social media marketing strategic planning?
What is the difference between a counter-controlled loop and a sentinel-controlled loop?
Identify the correct journal entries at the time of contracting the murabaha contract under the following scenario: An Islamic bank enters into a murabaha financing agreement for a plant at a cost of...
For the following exercises, sketch two periods of the graph for each of the following functions. Identify the stretching factor, period, and asymptotes. m(x) = 6csc(x+1) 3
A regular deposit of $100 is made at the beginning of each year for 20 years. Simple interest is calculated at i% per year for the 20 years. At the end of the 20-year period, the total interest in...
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.05 cm thick to a hemispherical dome with diameter 50 m.
Use the Chain Rule and the Product Rule to give an alternative proof of the Quotient Rule.
When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel: F = kR4....
The partners mehak and simran share in the profits and losses equally and their capital accounts have credit balance s of 1 5 0 0 0 and 2 5 0 0 0 respectively. The account balances for Mehak and...
LNS Corporation reports book profit of $ 2 , 0 0 0 , 0 0 0 . The $ 2 , 0 0 0 , 0 0 0 included $ 1 5 , 0 0 0 of tax exempt interest income, a capital loss of $ 2 , 0 0 0 , depreciation expense of $ 6...
Maggie Vitteta, single, works 3 8 hours per week at $ 1 9 . 0 0 an hour. How much is taken out for federal income tax?

Explain why ||A|| = max|aij| defines a norm on the space of n x n matrices. Show

Question:

Step by Step Answer:

If we identify a matrix A with a vect...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions