Show that if W1 W2 are finite dimensional subspaces of an inner product space, then W1

Question:

Show that if W1 ⊂ W2 are finite dimensional subspaces of an inner product space, then W1⊥ ⊃ W2⊥.

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 17, 2016 08:53 AM

See More Questions

Show that if w and Z are subspaces of V. then (a) Their intersection W Z is a subspace of V, (b) Their sum W + Z = { w + z | w W. z Z ) is also a subspace, but (c) Their union WUZ is not a...
Show that if W R3 is a subspace containing the vectors (1,2, - l)T, (2,0. l)T, (0,-1,3)T, then W = R3.
Show that if W is a subspace of a finite-dimensional vector space V, then W is finite-dimensional and dim W ( dim V.
What is food processing ? Different types of food processing methods Briefly explained
In general, courts are reluctant to grant shareholders petitions for corporate dissolution except in extreme circumstances, such as when corporate directors or shareholders are deadlocked and the...
State whether the following statements are true or false? If false, explain why. L01 (a) Fixed costs are those that do not vary with long-term changes in the level of sales or production. (b)...
Do you empathize with Mark, or do you feel that he simply has a bad attitude and has no business training new employees. Explain your answer in detail.
1. George Parker is trying to support the teachers in WTU by satisfying their needs. What needs is he focusing on by appealing the dismissals of teachers and threatening to file a lawsuit? 2. How do...
please help, thank you!! The income statements for Company A for Year 2 and Year 1 are presented below. Required: Prepare a vertical analysis of the data for Year 2 and Year 1 (Round your percentage...
The following is a list of 24 Marcos Pizza stores in Lucas County. The stores are identified by numbering them 00 through 23. Also noted is whether the store is corporate owned (C) or manager owned...
Let V be an inner product space. Prove that (a) = {0} (b) {0} = V
(a) Show that if W, Z Rn are complementary subspaces, then W and Z are also complementary subspaces. (b) Sketch a picture illustrating this result when W and Z are lines in R2.
What barriers to entry has Panera Bread created for potential competitors? How significant are these barriers?
Test the given claim. Assume that a simple random sample is selected from a normally distributed population. Use either the P-value method or the traditional method of testing hypotheses. Company A...
Trojan Technologies As Joyce Guo, senior buyer at Trojan Technologies Inc. in London, Ontario, Canada, finished her presentation, Randy Haill, materials manager, Made the following comments to her:...
In 2022, Andrew, who is single, has a comfortable salary from his job as well as income from his investment portfolio. However, he is habitually late in filing his federal income tax return. He did...
Express the confidence interval (0.045,0.123) in the form of p^ - E < p < p^+ E.
Boomtown is preparing a cost analysis of the three departments: Parks. Fire, and Water. To comply with accuracy standards in allocating indirect costs, Boomtown will employ the step-down method of...
Do the same exercise as in Question 8 but assume initially that 20% of people are below age 20, 20% are between ages 20 and 40, and 60% are between ages 40 and 60. Compare the answers to both...
Create an appropriate display of the navel data collected in Exercise 25 of Section 3.1. Discuss any special properties of this distribution. Exercise 25 The navel ratio is defined to be a persons...
The number of failures of a testing instrument from contamination particles on the product is a Poisson random variable with a mean of 0.02 failure per hour. (a) What is the probability that the...
A shipment of chemicals arrives in 15 totes. Three of the totes are selected at random, without replacement, for an inspection of purity. If two of the totes do not conform to purity requirements,...
The probability that your call to a service line is answered in less than 30 seconds is 0.75. Assume that your calls are independent. (a) If you call 10 times, what is the probability that exactly 9...
Suppose the S&P 500 currently has a level of 960. One contract of S&P 500 index futures has a size of $250 S&P 500 index. You wish to hedge an $800,000-portfolio that has a beta of 1.2. (A)In order...
Exhibit 4.1 The balance sheet and income statement shown below are for Koski Inc. Note that the firm has no amortization charges, it does not lease any assets, none of its debt must be retired during...
Haley is 57 years of age. She is planning for future long-term care needs. She knows that yearly nursing home costs in her area are currently $69,000, with prices increased by 5 percent annually....

Show that if W1 W2 are finite dimensional subspaces of an inner product space, then W1

Question:

Step by Step Answer:

If z W 2 then z w 0 for every w ...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions