Tagged Questions
1
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1answer
234 views
How to determine if a matrix is positive/negative definite, having complex eigenvalues?
I am trying to deal with an issue: I am trying to determine the nature of some points, that's why I need to check in Matlab if a matrix with complex elements is positive or negative definite. After ...
2
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2answers
62 views
Eigenvalues of a certain bordered identity matrix
Consider a complex $N-1 \times 1$ vector $b$ and a complex constant c. Let $I$ denote the $N-1 \times N-1$ identity matrix. Then what can we say about the eigenvalues of the matrix
\begin{align}
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2answers
48 views
eigenvalues for a complex matrix
How do you find the eigenvalues (hence the eigenvectors too) of a matrix with complex bits like this:
$$\hat{H}=\epsilon \begin{vmatrix} 0&i&0 \\\\ -i&0&0 \\\\ 0&0&-i ...
1
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0answers
48 views
complex eigenvalues of matrix sum
I have a set of (about 100) general real square matrices. Is it possible to determine whether none of their linear combinations has complex eigenvalues?
0
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1answer
139 views
Finding a matrix that has complex Eigenvalues
I have an assignment where I need to create 2x2 matrices for each of the following Eigenvalue pairs.
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1
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2answers
419 views
Raising a square matrix to the k'th power: From real through complex to real again - how does the last step work?
I am reading Applied linear algebra: the decoupling principle by Lorenzo Adlai Sadun (btw very recommendable!)
On page 69 it gives an example where a real, square matrix $A=[(a,-b),(b,a)]$ is raised ...
6
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1answer
859 views
intuition for complex eigenvalues
The eigenvalues of a rotation matrix are complex numbers. I understand that they cannot be real numbers because when you rotate something no direction stays the same.
My question
What is the ...
