Question: An n n matrix A is called nilpotent if an integer m exists with Am = On. Show that if is an eigenvalue

An n × n matrix A is called nilpotent if an integer m exists with Am = On. Show that if λ is an eigenvalue of a nilpotent matrix, then λ = 0.

Step by Step Solution

★★★★★

3.47 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

Suppose the l is an eigenvalue of A with corre... View full answer

blur-text-image
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)

Word file Icon

731-M-N-A-N-L-A (705).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

An n n matrix A is called nilpotent if Am = 0 for some m l. Show that = 0 is the only eigenvalue (even complex) of A, if A is nilpotent.

Q:

A square matrix A is called nilpotent if Ak = O for some k ¥ 1 (a) Show that is nilpotent. (b) Show that any strictly upper triangular matrix is nilpotent. (c) Find a nilpotent matrix which is...

Q:

A square matrix A is called nilpotent if Ak = O for some k 1. (a) Prove that the only eigenvalue of a nilpotent matrix is 0. (The converse is also true; see Exercise 8.6.18.) (b) Find examples where...

Q:

(5) A square matrix A is called nilpotent if there exists a positive integer k such that Ak = 0 where 0 is the zero matrix. If A is nilpotent n xn matrix and B is n x n matrix such that AB = BA. (a)...

Q:

\f3. An n x n matrix A is called nilpotent if there is some k 2 0 such that A* = 0. If ) is an eigenvalue of a nilpotent matrix A, show that A = 0.1. For each of the following matrices A, determine...

Q:

How to slove this question? Consider a matrix A with the special property that A"/ = Z for some integer m. Here Z is the zero-matrix (i.e. the matrix filled with zeroes). Such a matrix A is called...

Q:

hey guys, i need help coding B) and C) and easy code using python please l. Nilpotent Matrices 1. A matrix MMnn is called nilpotent if there is a positive integer n such that Mn=0, where 0 is the...

Q:

A and B are n n matrices. A square matrix A is called nilpotent if A m = O for some m > 1. (The word nilpotent comes from the Latin nil, meaning nothing, and potere, meaning to have power. A...

Q:

An n x n complex matrix A is called skew-hermitian if and only if: A = -A. A real, skew-hermitian matrix is called anti-symmetric or skew-symmetric. a) Let A be a skew-hermitian matrix and suppose A...

Q:

Math 636 Final - Quiz Component 1. The system of linear equations 2x2 x3 = 3 2x1 + x2 + 2x3 = 1 x1 + x2 + 3x3 = 2 (a) is consistent with a unique solution. (b) is consistent with infinitely many...

Q:

The Data in Concrete2 represent the compressive strength in thousands of pounds per square inch of 40 samples of concrete taken 2, 7, and 28 days after pouring. a. At the 0.05 level of significance,...

Q:

What methods are used to segment business-to-business markets?

Q:

What step ( s ) must precede the application of applicable discounts? a . Gather as much data as possible to support discounts b . Determine the base value of the equity or enterprise first c ....

Q:

You are managing a marketing project for a new product launch, and you have identified several stakeholders with different levels of interest and influence. Some stakeholders are supportive, while...

Q:

If f(x) = x + 4 and h(x) = 4x 1 , find a function such that g o f = h.

Q:

Suppose g is an even function and let h = f o g. Is h always an even function?

Q:

Suppose t is an odd function and let h = f o g. Is h always an odd function? What if f is odd? What if is f even?

Q:

The discussion of EFN in the chapter implicitly assumed that the company was operating at full capacity. Often, this is not the case. Assume that Rosengarten was operating at 9 0 percent capacity....

Q:

We have the following information of the firm and project cash flow. If the project has the same risk as the firm, is it a good project? Debt- Equity- Book value (millions) - 60 # of shares...

Q:

1. When he was CEO, Hurd wrote in the Standards of Business Conduct at HP that We want to be a company known for its ethical leadership.... His message in the preface continued: Let us commit...