For an n x n matrix A, the trace of A, Tr(A), is defined as the sum

Question:

For an n x n matrix A, the trace of A, Tr(A), is defined as the sum of the diagonal entries of A. Prove that the trace defines a linear transformation from Mnn to the vector space of all real numbers.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For book-img-for-question

Elementary Linear Algebra with Applications

ISBN: 978-0132296540

9th edition

Authors: Bernard Kolman, David Hill

See More Books

Question Posted: Jun 21, 2016 07:12 AM

See More Questions

The inverse of a matrix can also be computed by solving several systems of equations using the method of Example 3.34. For an n X n matrix A, to find its inverse we need to solve AX = In for the n...
The trace of an n X n matrix A = [aij] is the sum of the entries on its main diagonal and is denoted by tr(A). That is, tr(A) = a11 + a22 + + ann If A and B are n n matrices, prove the following...
Trace of a Matrix Using the following definition, prove the properties of the trace in Problems 1-3. The trace of an n x n matrix A = [aij], denoted Tr A, is the sum of the diagonal elements: 1....
The following is a comparative consolidated Statement of Financial Position for a particular firm X: Consolidated Balance Sheet (S in Millions) Current assets Cash and short-term investments Accounts...
Why should a project have a regular reporting period? Should all projects have the same reporting period? Why or why not? What types of data should be collected during each reporting period?
Assume that you bought an interest rate cap on three- month LIBOR with a 2.50 percent strike rate. The current rate for three- month LIBOR is 2.28 percent. a. What will happen to the premium (value)...
Water enters a 5 -ft-wide, 1 -ft-deep channel as shown in Fig. P4.66. Across the inlet the water velocity is \(6 \mathrm{ft} / \mathrm{s}\) in the center portion of the channel and \(1 \mathrm{ft} /...
Conventional and Dollar-Value LIFO Retail As of January 1, 2010, Aristotle Inc. installed the retail method of accounting for its merchandise inventory. To prepare the store's financial statements at...
Why would someone choose Business as a program of study? Explain, What would be the pros and cons of studying Business Administration? What are some future plans a graduate can do once their degree...
Choose one of the following contingency theories: 1) Houses Path Goal Theory (1971) 2) Hersey and Blanchards Situational Leadership Theory (1977) 3) Kerr and Jermiers Leadership Substitute Ideas...
Determine the matrix in homogeneous form that produced the image of the triangle depicted in the following figure: Original figure -4 -8
Let L1: V V and L2: V V be linear transformations on a vector space V. Prove that (L1 +L2)2 = L2 + 2L1 o L2 + L22 if and only if L1 o L2 = L2 o L1.
(a) Referring to Problem 1.69, calculate the total volume (in liters) of air an adult breathes in a day. (b) In a city with heavy traffic, the air contains 2.1 x 10-6 L of carbon monoxide (a...
Assuming the following declaration and initialization of variables, Determine the value assigned to the variable in each of the following assignment statements, or explain why it is not a valid...
What is the output from the following code segment? int[] [] intArray = {{2, 5, 4), (6, 3), (9, 7, 1, 5}}; (intArray [0].length); (int Array [2]. length); System.out.println System.out.println...
In Problem 4, the Vehicle, Car, and Truck classes were implemented. Vehicles could include more such as motorcycles, buses, trains, ships, and airplanes. Using UML diagrams, organize these vehicles....
Write a code segment to perform a sequential search on a one-dimensional array. Assume that the set of data could contain duplicates. If the item being searched for is found in the array, record the...
Nove Ltd is a large concern located in Hong Kong that manufactures a line of household appliances in which sales expansion in the past has been very rapid. Actual manufacturing takes place in...
For the following exercises, write a logarithmic equation corresponding to the graph shown. Use y = log 2 (x) as the parent function. IIII IIII 5- 4 3- -5-4-3 2 3 4 -2-
For a nonzero constant a, find the intercepts of the graph of (x 2 + y 2 ) 2 = a 2 (x 2 - y 2 ). Then test for symmetry with respect to the x-axis, the y-axis, and the origin.
The graph of f (x) = x2 - 2x - 1 is which of the following? -4 4-3-2-1.| 1 2 3 4 5 -5-4-3-2-1.112345 5-4-3-2-1 4 5 x -5-4- 2 3 4 5x
Find a such that f (x) = ax2 - 4x + 3 has a maximum value of 12.
Determine the leading term, the leading coefficient, and the degree of the polynomial. Then classify the polynomial function as constant, linear, quadratic, cubic, or quartic? a) g(x) = 1/23 x3 - 10x...
A cylindrical log is cut as shown to form a park bench. Find: a. The area of triangle OAB in m. [2] b. The volume of the log in m. [3] B 70% 40 cm 3m
Security issues in today's workplace. Identify the different types of potential security issues an employer may have to deal with. Give examples to illustrate each of these potential security...
Research on the Internet and identify an emerging security issue. Describe the issue and its origin. Provide an example of this new security issue. Discuss the impacts of the security issue and...

For an n x n matrix A, the trace of A, Tr(A), is defined as the sum

Question:

Step by Step Answer:

Let A and B belong to M nm and let c be a ...View the full answer

Elementary Linear Algebra with Applications

Students also viewed these Linear Algebra questions