Q - Linear Algebra II TT23 Collection, Q2


Flashcards

What are the eigenvalues of

\[\begin{pmatrix} 1 & 1 & \cdots & 1 \\\\ 1 & 1 & \cdots & 1 \\\\ \vdots & \vdots & \ddots & \vdots \\\\ 1 & 1 & \cdots & 1 \end{pmatrix} \in \mathbb R^{n \times n}\]

?


\[\\{0, 0, \ldots, 0, n\\}\]

where $0$ is repeated $n-1$ times.

Suppose $A$ is a matrix with eigenvalues given by $\lambda _ i$. Then what are the eigenvalues of the matrix $A - cI$ where $c$ is a constant?::

\[\lambda_i - c\]

Quick! What are the eigenvalues of

\[\begin{pmatrix} 1 & 2 & 2 \\\\ 2 & 1 & 2 \\\\ 2 & 2 & 1 \end{pmatrix}\]

?


\[{-1, -1, 5}\]

Proofs




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