# Tagged Questions

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### 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 ...
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### 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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### 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 ...
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### 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?
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### 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. ...
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 ...