Question: Show that M = A + iB (A and B real matrices) is skew Hermitian if and only if A is skew symmetric and B

Show that M = A + iB (A and B real matrices) is skew Hermitian if and only if A is skew symmetric and B is symmetric.

Step by Step Solution

★★★★★

3.34 Rating (166 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

M H A iB T A T iB ... 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

949-M-L-A-E (835).docx

120 KBs Word File

Students Have Also Explored These Related Linear Algebra Questions!

Q:

If IA is the moment of inertia of a mass distribution of total mass M with respect to an axis A through the center of gravity, show that its moment of inertia IB with respect to an axis B, which is...

Q:

A set E in [a, b] is said to be (Lebesgue) measurable if its characteristic function 1E (defined by 1(x) := 1 if x E and 1(x) := 0 if x [a, b]\E) belongs to M[a, b]. We will denote the collection...

Q:

Show that if A is skew Hermitian and is an eigenvalue of A then is purely imaginary (i.e., = bi, where b is real).

Q:

At many points in the course, we have made assumptions that various matrices or eigenvalues are real while discussing various theorems. If you have noticed, this has always happened in contexts where...

Q:

1. (4 Points) Let x and y be vectors in R". None of the given choices. O If [x) + lyl = [x + yl. then x and y are parallel. If x . y = 1, then x and y are parallel. O If [x x yl = 1, then x and y are...

Q:

Ministry of Higher Education Kingdom of Saudi Arabia CSTS SEU, KSA Linear Algebra (Math 251) Level IV, Assignment 3 (2016) 1. State whether the following statements are true or false: [6] (a) The sum...

Q:

[Q8] (Section 5.4: The Spectral Theorem) Recall that a matrix A e Cox is called normal if AA* = A*A, where A* is the conjugate transpose of A. If A e R"*", then this condition is AA" = A'A. The class...

Q:

*(Important Note) Please explain thoroughly and show your work in each question including how you get the mean, standard deviation and the sketches with your data. No rush and take your time to get...

Q:

(a) Prove that the commutator of two upper triangular matrices is upper triangular. (b) Prove that the commutator of two skew symmetric matrices is skew symmetric. (c) Is the commutator of two...

Q:

QUESTION 2 Given matrix A below, -2 3 0 -20 0 3 4 a- (6 pts.) What are the eigenvalues of A? b- (6 pts.) What are the eigenspaces corresponding to each eigenvalue? c- (6 pts.) What are the basis...

Q:

The range for a set of data is estimated to be 36. a. What is the planning value for the population standard deviation? b. At 95% confidence, how large a sample would provide a margin of error of 3?...

Q:

Consider again the conditions of Exercise 13. Are the scores of college students on the mathematics test and the music test positively correlated, negatively correlated, or uncorrelated?

Q:

*BE3.12 (LO 4, 6) Using the information from BE3.11, prepare a retained earnings statement for the year ended December 31, 2025. Assume an error was discovered: Land costing NT$80,000 (net of tax)...

Q:

3. Explain why a government policy maker cannot afford to ignore economic theory.

Q:

Use the properties of Section 3.2 to prove that laa

Q:

Theorem 3.8 assumes that all calculations for det(A) are done by exact arithmetic. As noted previously, this is usually not the case in software. Hence, computationally, the determinant may not be a...

Q:

Let A be an n ( n matrix. (a) Show that ((t) = det(t In - A) is a polynomial in t of degree n. (b) What is the coefficient of tn in ( (t)? (c) What is the constant term in ((t)?

Q:

During a job interview, Pam Thompson is offered a salary of $95,000. The company gives annual raises of 5 percent. What will be Pam's salary during her fifth year on the job? Use Exhibit 1-A. (Round...

Q:

You are CEO of a high-growth technology firm. You plan to raise $220 million to fund a planned expansion by issuing either new shares or new debt. With the expansion, you expect earnings next year of...

Q:

For SFRFP bonds calculate YTM on January 18, 2017 (day of the print of the table in the WSJ). 3. For SEREP bonds calculate YTM on January 18, 2017 (day of the print of the table in HIGH YIELD ISSUES...