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Exercise 2.4.18

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Matrix

A = [\begin{matrix} 1 & 1 & 1 \\ 1 & 2 & 2 \\ 1 & 2 & 3 \end{matrix}]

has $a_{ij} = \min (i, j)$ .

Matrix

A = [\begin{matrix} 1 & - 1 & 1 \\ - 1 & 1 & - 1 \\ 1 & - 1 & 1 \end{matrix}]

has $a_{ij} = {(- 1)}^{i + j} =$ "alternating sign matrix".

Matrix

A = [\begin{matrix} 1 ∕ 1 & 1 ∕ 2 & 1 ∕ 3 \\ 2 ∕ 1 & 2 ∕ 2 & 2 ∕ 3 \\ 3 ∕ 1 & 3 ∕ 2 & 3 ∕ 3 \end{matrix}]

has $a_{ij} = i ∕ j$ . This will be an example of a rank one matrix : 1 column ${[\begin{matrix} 1 & 2 & 3 \end{matrix}]}^{T}$ multiplies 1 row $[\begin{matrix} 1 & \frac{1}{2} & \frac{1}{3} \end{matrix}]$ .

mathchakra

2021-12-06 17:39

Exercise 2.4.18

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