Let A be an m x n matrix whose columns are nonzero, mutually orthogonal vectors in Rm.

Question:

Let A be an m x n matrix whose columns are nonzero, mutually orthogonal vectors in Rm.
(a) Explain why m > n.
(b) Prove that AT A is a diagonal matrix. What are the diagonal entries?
(c) Is A AT diagonal?

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 08:49 AM

See More Questions

Let A be an m x n matrix whose column vectors are mutually orthogonal, and let b Rm. Show that if y is the least squares solution to the system Ax = b then b' a
Let w1,... wn be any basis of the subspace W Rm. Let A = (w1,...,wn) be the m x n matrix whose columns are the basis vectors, so that W = rng A and rank A = n. Let P = A(AT A)-1 AT be the...
Let A be an m x n matrix with singular value decomposition UVT. Show that for any vector x Rn n ||x|| ||Ax||2 l||x||2
What is the final pressure of a gas whose initial conditions are 1.407 L, 2.06 atm, and 67C and whose final volume and temperature are 608 mL and 449 K, respectively? Assume the amount remains...
Oakwood Outpatient Clinic is analyzing its operation in an effort to improve performance. The clinic estimates that a patient spends on average 3 hours at the facility. The amount of time the patient...
A media rental store rented the following number of movie titles in each of these categories: 170 horror, 230 drama, 120 mystery, 310 romance, and 150 comedy. If a person selects a movie to rent,...
A customer has sent a rotor to your shop for balancing. The balance specification calls for less than 1 mil vibration. How would you proceed?
Mauro Products distributes a single product, a woven basket whose selling price is $15 and whose variable expense is $12 per unit. The companys monthly fixed expense is $4,200. Required: 1. Solve for...
An electron travels in a circle perpendicular to a magnetic field. (Recall m = 9.1x10 -31 kg and qe = 1.6x10 -19 C.) The speed of the electron is 200m/s and the radius of the circle is 0.1m....
In a certain city, 30% of the families have a MasterCard, 20% have an American Express card, and 25% have a Visa card. Eight percent of the families have both a MasterCard and an American Express...
Suppose u1,.......,uk form an orthonormal set of vectors in Rn with k < n. Let Q = (u, u2 ... uk) denote the n k matrix whose columns are the orthonormal vectors. (a) Prove that QT Q = Ik. (b) Is...
Let K > 0 be a positive definite n x n matrix. Prove that an n n matrix S satisfies ST K S = I if and only if the columns of S form an orthonormal basis of Rn with respect to the inner product (v,...
A rectangular closed box is to be built at minimum cost to hold 125 m 3 . Since the cost will depend on the surface area, find the dimensions that will minimize the surface area of the box.
What are the 4 + 1 views of architecture in the Unified Process?
What are the benefits of adopting an architecture-centric approach?
Pick a company or brand or business on which to focus, such as cereals, What are the major segments? What are the customer motivations by segments? What are the unmet needs?
What are the disadvantages of the closed layered architecture?
What is the difference between an architectural view and an architectural viewpoint?
The eighth step in the accounting cycle is to journalize and post the closing entries: Closing is the process of transferring the balances in the temporary accounts to the owners capital account. ...
Graph the following conic sections, labeling vertices, foci, directrices, and asymptotes (if they exist). Give the eccentricity of the curve. Use a graphing utility to check your work. 10 5 + 2 cos 0
(-8x + 5y 12) 6(2x 4y 10)
Evaluate 2x squared when x = 5 and when x = -5
[6(x + 4) 12] [5(x 8) + 14]
There are two real numbers a for which (2x)+15 (1-x) = 8x - 3x + 2. The sum of these two real numbers is
Net sales Cost of goods sold Depreciation INCOME STATEMENT (Figures in $ millions) Earnings before interest and taxes (EBIT) Interest expense Income before tax Taxes Net income $ 882.00 742.00 32.00...
Venita is sewing new curtains. The table below shows the relationship between the number of stitches in a row and t length of the row. Sewing Number of Length (cm) stitches 5 1 15 3 20 4 30 6 What is...

Let A be an m x n matrix whose columns are nonzero, mutually orthogonal vectors in Rm.

Question:

Step by Step Answer:

a Assuming the columns are nonzero Proposition 54 implies they are linearly independent But th...View the full answer

Applied Linear Algebra

Students also viewed these Linear Algebra questions