Question: Prove that the map p: V ! V is the projection into M along N if and only if the map id-p is the projection

Prove that the map p: V ! V is the projection into M along N if and only if the map id-p is the projection into N along M. (Recall the definition of the difference of two maps: (id-p)

(id-p) (V) = id(v) p(v) = v- p(v).)

Step by Step Solution

★★★★★

3.41 Rating (164 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

If V M N then every v... View full answer

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)

961-M-L-A-L-S (5584).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Prove that the map in Example 1.9, from P5 to P5 given by p(x) p(x - 1), is a vector space isomorphism.

Let t: V V be a linear transformation and suppose v V is such that tk(v) = 0 but tk-1(v) 0. Consider the t-string hv, t(v),....., tk-1(v)i. (a) Prove that t is a transformation on the span of the...

The commutator of two linear transformations L, M: V V on a vector space V is defined as K = [L, M) = L M - M L. (7.15) (a) Prove that the commutator K is a linear transformation. (b) Prove that L...

QUIZ... Let D be a poset and let f : D D be a monotone function. (i) Give the definition of the least pre-fixed point, fix (f), of f. Show that fix (f) is a fixed point of f. [5 marks] (ii) Show that...

In a Hopfield neural network configured as an associative memory, with all of its weights trained and fixed, what three possible behaviours may occur over time in configuration space as the net...

For monotone functions f, f0: P Q between posets (P, vP ) and (Q, vQ), let f v f(i) Prove that the binary relation v is a partial order. [3 marks] (ii) For monotone functions between posets p : P 0...

Consider the trigonometric series a0 2 + X r=1 (ar cos rx + br sin rx) where a0, a1, a2, . . . and b1, b2, . . . are constants and suppose that f(x) is a periodic function of x with period 2. (a)...

In this question you will be asked to reflect on a project you have been involved in or observed, in which a design evolved, or could have evolved, through applying a theory of user behaviour. You...

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Let i and j be positive integers. (i) Prove that there exist natural numbers a and b such that ai = bj+gcd(i, j). You may use standard results provided that you state them clearly. [4 marks] (ii) Let...

Read the "Role of an Athletic Director case study and put yourself in Marisol's position. In an essay of 1,000-1,250 words, answer the following questions: 1. What are the first things you should do...

Use the table to the right to find the given derivative. a dx f(x)g(x) d [f(x)g(x) dx X (Simplify your answer.) ew an example. Textbook Clear all X f(x) f'(x) g(x) g'(x) 1 2 3 3 5 4 4 1 2 3 5 5 4 1 2...

Which of the following is defined as the data generated by a system or subsystem that is used to monitor its performance or state of health? A Zeroization B Telemetry Metadata D Data remanence

A Level Effects Model of UK Gilts Gauss file(s) sim_ukgilts.g, ukgilts.dat Matlab file(s) sim_ukgilts.m, ukgilts.mat For the data on UK gilts, rt , consider the model drt = ( rt)dt + r t dB , dB ...

The eigenvector shortcut of Problem 17 may fail when h = 0, forcing a return to the definition Av = Î»v to find the eigenvector(s). For each eigen-value in the following matrices, find...

For each matrix in Problems a to b compute its eigenvalues, eigenvectors and the dimension of each eigenspace. a. b. 2 00 12 -1 0 12-1 4 -4 5

Show that the set of eigenvectors belonging to a particular eigenvalue of an n x n matrix, together with the zero vector, is a subsiace of 1121.

Watson Oil recently reported (in millions) $8,250 of sales, $5,750 of operating costs other than depreciation, and $1,400 of depreciation. The company had $3,200 of outstanding bonds that carry a 5%...

2. Provide the most recent available 'profit' data for the following healthcare entities: (5 points) a. Two pharmaceutical companies. b. Two insurance companies. c. Two hospitals or hospital's chains

Problem Solving Tort Mike runs a small bicycle repair business as a sole trader. He does everything himself; he fixes customers bikes and does all the bookkeeping, etc, for the business. Simon...