eigenvalues

Let $M = \begin{pmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{pmatrix}$ be a $2 \times 2$ matrix, where $\theta = \frac{2\pi}{5}$, and $I_2 = \begin{pmatrix...

Let $\gamma_1, \gamma_2, \gamma_3$ be the eigenvalues of the matrix $\begin{bmatrix} 1 & 0 & 0 \\ 0 & \cos t & \sin t \\ 0 & -\sin t & \cos t \end{bmatrix}$, where $t \in [-\pi, \p...

Let A = $(I_n - \frac{1}{n} \mathbf{1} \mathbf{1}^T)$ be a matrix, where $\mathbf{1} = (1,1,1, ...,1)^T \in \mathbb{R}^n$ and $I_n$ is the identity matrix of order n. The value of...