# Tagged Questions

63 views

### What's the formula matrix with complex numbers?

Given$$\mathbf{M}= \begin{pmatrix} 7 & 5 \\ -5 & 7 \\ \end{pmatrix}$$, what's the formula matrix for $\mathbf{M}^n$? The eigenvalues and eigenvectors are ...
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### Are complex eigenvalues special?

I've noticed that complex eigenthings are treated as a whole separate topic to real eigenthings (I say things to mean values and vectors). I see no reason for this distinction, yes it makes the ...
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### Determining rotation axis for matrix with complex eigenvectors.

I'm using Zhang's method to determine the 3D camera parameters from a set of images. When calculating extrinsic parameters for the third image, I get the following matrix.  \begin{vmatrix} ...
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### Finding diagonal and unitary matrices

Let $A=\begin{pmatrix} 1 & 1+i\\ 1-i & 2 \end{pmatrix}$ I'm trying to find a diagonal matrix $D$ and a unitary matrix $U$ so that $U^\star AU=D$. (We define $U^*=\overline{U}^t$ ). I ...
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### What are the Complex (Non-Real) Eigenvectors of $3\times 3$ Rotation Matrices?

A $3\times 3$ rotation matrix $R$ that rotates $\mathbb{R}^3$ around the unit vector $v\in\mathbb{R}^3$ by angle $\theta$ (as defined by Rodrigues' rotation formula) satisfies the ...
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### Complex conjugates and complex eigenvalues

Suppose the matrix A with real entries has complex eigenvalues $\lambda = \alpha + i\beta\,$ and $\overline{\lambda} = \alpha - i\beta\,$. Suppose that $Y_0 = (x_1 + iy_1, x_2 + iy_2)$ is an ...
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 ...