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Linear Algebra and Learning from Data

Exercise 1.7.26

Answers

1.
The determinant of $S$ is the product of eigenvalues: 10
1.
The eigenvalues of $S$ : $2, 5$
1.
The eigenvectors of $S$ : $x_{1} = [\begin{matrix} \cos 𝜃 \\ \sin 𝜃 \end{matrix}]$ and $x_{2} = [\begin{matrix} - \sin 𝜃 \\ \cos 𝜃 \end{matrix}]$
1.
A reason why $S$ is symmetric positive definite: This is because $S$ can be expressed as $A^{T} A$ where $A$ has independent columns.

niuers

2020-03-20 00:00

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