Let u and v be nonzero vectors in R. In Section 5.3 we defined the angle between

Question:

Let u and v be nonzero vectors in R". In Section 5.3 we defined the angle between u and v to be the angle Î¸ such that

A linear operator L: Rn †’ Rn is called angle preserving if the angle between u and v is the same as that between L(u) and L(v). Prove that if L is inner product preserving (see Exercise 16), then it is angle preserving.

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: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:12 AM

See More Questions

Let u and v be nonzero vectors in a vector space V. Show that u and v are linearly dependent if and only if there is a scalar k such that v = ku. Equivalently, u and v are linearly independent if and...
Let a and b be nonzero vectors in Rn. a) If (t) = a + tb for t R, show that for each to, t0, t1, t2 R with t1, t2 t0, the angle between (t0) - (t0) - (t0) and (t2) - (t0) is 0 or . b) If is the...
Let L: R2 R2 be the linear operator defined by (a) is In Ker L? (b) is In Ker L? (c) Is In range L? (d) is In range L? (e) Find Ker L (f) Find a set of vectors spanning range L. 21u u1 42 4) L112 2 3...
Consider the following graph. 2 7 6 C 10 10 H 11 E 12 15 14 (a). Find a minimum spanning tree of the graph using Kruskal's algorithm. List the edges in the order they are put into the tree. (b)....
Calculate the ES, EF, LS, and LF times and the slack for each activity in the figure below and identify the critical path for the project. Can the project be completed in 30 weeks? Discuss.
The typical low balance customer at your bank with an average monthly demand deposit balance under $ 175 exhibits the following monthly activity: 35 withdrawals (11 electronic), two transit checks...
Figure P4.64 shows a fixed control volume. It has a volume $V_{0}=1.0 \mathrm{ft}^{3}$, a flow area $A=1.0 \mathrm{ft}^{2}$, and a length $\ell_{0}=1.0 \mathrm{ft}$. Position $x$ represents...
Adjustment data for Ms. Ellen's Laundry Inc. for the year ended December 31, 20Y8, are as follows: a. Wages accrued but not paid at December 31, $2,150 b. Depreciation of equipment during the year,...
Perhaps you can recall your first day as a new student or employee in a child care center. How did you feel on that first day? What else do you wish you had known about the center or the program? Do...
Write a program that creates a Date object, sets its elapsed time to 10000, 100000, 1000000, 10000000, 100000000, 1000000000, 10000000000, and 100000000000, and displays the date and time using the...
Let L1: V V and L2: V V be linear transformations on a vector space V. Prove that (L1 +L2)2 = L2 + 2L1 o L2 + L22 if and only if L1 o L2 = L2 o L1.
Let L: V W be a linear transformation. If {v1, v2,..., vk} spans V, show that {L(v,), L(v2),..., L(vk)} spans range L.
In exercise find the limit L. Then find > 0 such that |(x) -L| < 0.01 whenever 0 < |x -c| < . lim (x + 6) x-4
Using the array intArray described in the previous exercise, write a code segment to output all the even numbers in the array, regardless of their position in the array.
A store is having a sale and items are either 30,50 , or $70 \%$ off. Assuming all the items priced between $\$ 5.00$ and $\$ 50.00$ are on sale, output the following table using nested loops....
Rewrite the following for loop as a A. while loop *B. do-while loop int total, count; total = 0; for (count = 1; count
A part of the LineSI class from Section 5.6.1 is shown below. Identify necessary and unnecessary use of the keyword this. public class LineSI { // data members private static final double...
The Supreme Canning Company (the true name of the company is disguised) is an independent US packer of tomato paste and other tomato products (whole peeled tomatoes, chopped tomatoes, tomatoes and...
For the following exercises, refer to Table 11. Graph the logistic equation on the scatter diagram. x 1 f(x) 8.7 2 12.3 3 4 5 15.4 18.5 20.7 Table 11 6 22.5 7 23.3 8 9 10 24 24.6 24.8
The Ferris wheel in the figure has a radius of 68 feet. The clearance between the wheel and the ground is 14 feet. The rectangular coordinate system shown has its origin on the ground directly below...
Use substitution to determine whether 2, 3, and - 1 are Zeros of f(x) = 2x3 - 3x2 + x + 6?
Use substation to determine wheter 2, 3, and - 1 are zeros of g(x) = x4 - 6x3 + 8x2 + 6x - 9?
Use substitution to determine whether 1, -2, and 3 are zeros of g(x) = x4 - x3 - 3x2 + 5x - 2?
Mary would like to save $10,000 at the end of 5 years for a future down payment on a car. How much should she deposit at the end of each month in a savings account that pays 1.2%/a, compounded...
AA stock price is $45/share. The stock is expected to pay dividends $2.50 in the coming year. After reviewing all information, you concluded: the price one year from now will be $50/share and you...
Fung is planning for the correct after tax and after inflation real rate of return to use. If inflation will be 1.3%, the average rate of return on his investments will be 4.9%, and the tax rate on...

Let u and v be nonzero vectors in R. In Section 5.3 we defined the angle between

Question:

(u, v) cos θ =

Step by Step Answer:

If Lu Lv u v then Wher...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions