# Tagged Questions

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### Diagonalization with the given eigenvalue and its vector

Let $-3$ be an eigenvalue of a $3\times3$ singular matrix $P$ and $$P\begin{bmatrix} 5\\ 3\\ -2 \end{bmatrix}=\begin{bmatrix} -20\\ -12\\ 8 \end{bmatrix}.$$ Then find whether $P$ is ...
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### Eigenvaluse and eigenvectors of differential equation

Vector space $C_2$ consists of every function that's second derivative is continuous in [0,1]. Tensor $A$ on the space $C_2$ is defined as $Ay=\frac {d^2 y}{dt^2}$ where $y(t)$ is a vector on space ...
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### Eigenvector when all terms in that column are zero?

so I have this matrix: $$\begin{matrix} 0.7 & 0 & 0 \\ 0.1 & 0.6 & 0 \\ 0 & 0.2 & 0.8 \\ \end{matrix}$$ I managed to solve ...
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### Eigenvalues of a rank 2 tensor defined by an integral

I've been given the question: "Consider the tensor: $$C_{ij}=\int_{V}{x_ix_j|\mathbf {x}|^2 + x_ix_j(\mathbf {x.n})^2} dV$$ where V is the volume of a sphere radius R centred on the origin. What ...
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### Prove that adjacency matrix has negative eigenvalue

We are given non-oriented graph without loops. Task is to prove that adjacency matrix of that graph has negative eigenvalue. I put some effort into drawing a proof here , but it seems that I'm ...
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### Does this question make any sense - eigenvalues and norms

Im having difficulties understanding this question: show that if $b$ is an eigenvector of an invertible matrix $A$ with an eigenvalue $\lambda_1$ and $\delta b$ is an eigenvector of $A$ with an ...