(a) Let U be a m n matrix and V an n m matrix, such...

Question:

(a) Let U be a m × n matrix and V an n × m matrix, such that the m × m matrix I_m+ U V is invertible. Prove that I_n +V U is also invertible, and is given by

(b) The Sherman–Morrison–Woodbury formula generalizes this identity to

Explain what assumptions must be made on the matrices A,B, U, V for (1.42) to be 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: 9783319910406

2nd Edition

Authors: Peter J. Olver, Chehrzad Shakiban

See More Books

Question Posted: Apr 15, 2023 07:01 AM

See More Questions

Matrix multiplication interacts nicely with many operations. But not always with transforming a matrix to reduced row-echelon form. Suppose that A is an m n matrix and B is an n p matrix. Let P be...
Let S be an m n matrix and let b Rm. Show that b R(A) if and only if b =AA+b
Let A be an m n matrix and let c be a scalar. Show that if c A =0, then either c = 0 or A = O.
A portfolio manager owns a bond worth 2,000,000 that will mature in one year. The pound is currently worth $1.65, and the one-year future price is $1.61. If the value of the pound were to fall, the...
At the beginning of 2016, Hill Manufacturing purchased a new computerized drill press for $75,000. It is expected to have a five-year life and a $15,000 salvage value . Required a. Compute the...
From the standpoint of the borrower, is long-term or short-term credit riskier? Explain. Would it ever make sense to borrow on a short-term basis if short-term rates were above long-term rates?
Assume a population of checks numbered 4001 to 6000 . Indicate the first five numbers to be selected from the random number table in Figure 5-1, if the auditor uses the second set of four digits,...
An athlete carefully watches her intake of calcium, protein, and calories. Her breakfast diet consists mainly of milk and cereal, whose prices and nutrient contents appear in the following table: She...
Explain how culture can be used to generate a competitive advantage in a multinational organization.?
The shaft shown in the figure is driven by a gear at the right keyway, drives a fan at the left keyway, and is supported by two deep-groove ball bearings. The shaft is made from AISI 1020 cold-drawn...
True or false: A square matrix that has a column with all 0 entries is singular. What can you say about a linear system that has such a coefficient matrix?
(a) Write down the 5 5 identity and zero matrices. (b) Write down their sum and their product. Does the order of multiplication matter?
Determine whether the graph represents a function. If it does represent a function, give its domain and range. y- 15- -15 15 x -15+
Describe five key steps that an operational auditor should perform when auditing an organizations PMO.
Relate the three main forms of resistance to Situational Positioning and how awareness of this impacts risk assessments.
The Taylor Rule puts as much weight on closing the unemployment gap as it does on closing the inflation gap. a. just b. twice c. half d. ten times
How does W. Edwards Demings Plan step relate to project management and how can operational auditors verify that management has effectively implemented this step?
What are the implications of Kurt Lewins Step 3: Refreeze for operational auditors and how can they verify that management has effectively implemented this step?
Which of the following is matter and not matter? 1. The moon 2. An idea for a new invention
Perform the operation by first converting the numerator and denominator to scientific notation. Write the answer in scientific notation. 7,200,00/0.000009
Explain why the solution to the homogeneous system Ax = 0 with nonsingular coefficient matrix is x = 0.
Write out the details of the proof of the "if" part of Theorem 1.7: if A is nonsingular, then the linear system Ax = b has a unique solution for every b. Theorem 1.7 A linear system Ax = b has a...
Write down the elementary 4 4 permutation matrix (a) P1 that permutes the second and fourth rows, and (b) P2 that permutes the first and fourth rows. (c) Do P1 and P2 commute? (d) Explain what the...
Greg Thomas purchased one - half of Ian Hamilton s interest in the Freidman and Hamilton partnership for $ 4 9 , 5 0 0 . Prior to the investment, land was revalued to a market value of $ 1 8 9 , 2 0...
What are the two basic timing strategies? What is the intent of each? If nontax factors are irrelevant, what is the best course of action in timing strategy when you expect tax rate to increase in...
You are provided with the following summarised information relating to Virgo Limited, a wheel caps and rims distributor: Statement of Financial Position ( balance sheet ) as at 3 1 December 2 0 1 9 :...

(a) Let U be a m n matrix and V an n m matrix, such...

Question:

(In + VU)¹= In - V(Im + UV)-¹ U.

Step by Step Answer:

a To prove that In VU is invertible we need to show that there exists a matrix M such that In VUM MI...View the full answer

Applied Linear Algebra

Students also viewed these Mathematics questions