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Linear Algebra and Learning from Data

Exercise 1.7.13

Answers

$A = [\begin{matrix} 1 & 2 \\ 0 & 3 \end{matrix}]$ : $A^{T} A$ is positive definite since $A$ has independent columns
$A = [\begin{matrix} 1 & 1 \\ 1 & 2 \\ 2 & 1 \end{matrix}]$ : : $A^{T} A$ is positive definite since $A$ has independent columns
$A = [\begin{matrix} 1 & 1 & 2 \\ 1 & 2 & 1 \end{matrix}]$ : : $A^{T} A$ is not positive definite since column 3 is a combination of column 1 and column 2

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2020-03-20 00:00

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