Homework 3 collaboration area
Question from student regarding HW #3:
When the directions state to find the spectrum, is it asking for the spectrum of the original matrix or the spectrum of the symmetric, skew-symmetric, orthoganal, hermitian, skew-hermitian, or unitary matrix?
Answer from Bell:
You'll find the definition of the spectrum on page 334. It is just another word for the set of all eigenvalues. The problem is asking you to find the spectrum for the original matrix. Then determine the type of the matrix and verify if the eigenvalues satisfy the conditions of Theorems 1 and 5.
Question from student regarding HW#3:
How much detail is sufficient on page 339, problem 30?
Answer from Bell:
You'll need to explain in words, using results from the book as evidence to back up your statements. It will take three or four sentences to explain and your explanation should convince anyone who has read the book that you are correct. If somebody else in the class reads your explanation, they should say, oh yes! That makes perfect sense.
Question from student:
I am stuck on where to start with HW3, lesson 7, #30, the proof that the inverse of a square matrix exists iff no eigenvalues are zero.
Answer from Bell:
Start with the definition of an eigenvalue. If r is an eigenvalue, then
det(A-rI)=0.
If r=0, what does that equation say about the matrix A?
Question from student:
I'm have a couple of issues. First of all, problem 11 on p 348 is asking if the matrix is symmetric, skew-symmetric, or orthogonal.. I found the eigenvalues to be a repeated real root, but the matrix is neither of the 3. Also problem 12 has some really nasty eigenvalues, am I doing something wrong?
