Question: Prove that the diagonal matrices form a subspace of Mnn. What is its dimension?

Prove that the diagonal matrices form a subspace of Mn×n. What is its dimension?

Step by Step Solution

★★★★★

3.38 Rating (160 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

The set of diagonal matrices is nonempty as ... 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

961-M-L-A-L-S (5495).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

If the X and Y coordinates (in feet) of station A are (5000.00, 5000.00), what are the coordinates of the remaining labeled corners in the accompanying figure? 430.00 ft, S 8959 E 46 41 LUI G Radius,...

Q:

A complex matrix H is called Hermitian if it equals its Hermitian adjoint, W = H, as defined in the preceding exercise. (a) Prove that the diagonal entries of a Hermitian matrix are real. (b) Prove...

Q:

Let A be an m n matrix. (a) Describe the diagonal entries of AT A in terms of the columns of A. (b) Prove that the diagonal entries of AT A are nonnegative. (c) When is AT A = O?

Q:

Prove: If A and B are n n diagonal matrices, then AB = BA.

Q:

In all this problem, the matrices are square. 1- Prove that the set of squares matrices M, (R) is an algebra with dimension n and gives a basis of it. 2- Prove that the subset of invertible matrices...

Q:

Please answer questions 10 , 12 , 13 , and 17. U1: 1 ,022 1 #232 O 5 1 3 Find the transition matrix from B to B'. What could be the transition matrix from B' to B? 11. Are these three vectors in R4...

Q:

Please answer questions 3 , 5 , 6 , 7, and 8 only. U1: 1 ,022 1 #232 O 5 1 3 Find the transition matrix from B to B'. What could be the transition matrix from B' to B? 11. Are these three vectors in...

Q:

A square matrix is symmetric if each i, j entry equals the j, i entry, that is, if the matrix equals its transpose. (a) Prove that for any square H, the matrix H + HT is symmetric. Does every...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

chapter 5 INTRODUCTION TO MATRIX ALGEBRA GOALS The purpose of this chapter is to introduce you to matrix algebra, which has many applications. You are already familiar with several algebras:...

Q:

1 1. (6+4+4+6) Let P3 denote the vector space of all third degree or less polynomials. (a) Find two linearly independent vectors in P3 that interpolate the data points (1, 2), (2, 1) and (3, 2). (b)...

Q:

A mine needs to build an evaporation pond to ensure that runoff from the mine site does not enter the surrounding environment i.e. all the runoff from the site is to be evaporated. The volume of...

Q:

In February 2001, currency held by individuals and businesses was $537.1 billion; traveler's checks were $8.0 billion; checkable deposits owned by individuals and businesses were $544.9 billion;...

Q:

Question content area top Part 1 Match the description with the correct information characteristic. ( Not all information characteristics may be used. ) Question content area bottom Part 1...

Q:

Name the financial statement (balance sheet, income statement, statement of changes in equity, statement of cash flows) on which each of the following items would appear. Indicate the part of the...

Q:

Zero Corporation contributes inventory (computers) to State University for use in its mathematics program. The computers have a $1,225 cost basis and an $2,800 FMV. How much is Zeros charitable...

Q:

A five-year bond with a yield of 11% (continuously compounded) pays an 8% coupon at the end of each year. a) What is the bonds price? b) What is the bonds duration? c) Use the duration to calculate...

Q:

Carver Corporation uses the accrual method of accounting and the calendar year as its tax year. Its board of directors authorizes a cash contribution on November 3 of Year 1, that the corporation...

Q:

Heritage Gardens provides complete garden design and landscaping services. The company uses a job-order costing system to track the costs of its landscaping projects. The table below provides data...

Q:

3. A political scientist asks voters leaving the polling center for whom they voted in the city council election; she plans to compare her data to the actual voting outcome. Why should the researcher...

Q:

Commuters In Problems 1-2, find all the 2 x that commute with the given matrix. 2 matrices. 1. Where a ( R 2. Where k ( R, k ( 0 3 0 0 0 0

Q:

Products with Transposes Use matrices And To find the indicated products for parts (a) - (d). (a) ATB (b) ABT (c) BTA (d) BAT A- 4

Q:

Reckoning In Problems 1-3, prove the statements form x matrices A and Band scalars c and d? 1. A - B = A +(-l)B 2. A + B = B + A 3. (c + d)A = cA + dA?

Q:

Time spent using e-mail per session is normally distributed, with u = 8 minutes and o = 2 minutes. If you select a random sample of 25 sessions, a. what is the probability that the sample mean is...

Q:

Bottoms Up Diaper Service is considering the purchase of a new industrial washer. It can purchase the washer for $6,300 and sell its old washer for $2,100. The new washer will last for 6 years and...

Q:

Samson Company had the following transactions. 1. Issued 5,000 shares of $100 par preferred stock at $107 for cash. 2. Issued 8,000 share of common stock with a par value of $10 for $120,000. 3....