Exercise 1.2.2

Question

Suppose $\boldsymbol{a}$ and $\boldsymbol{b}$ are column vectors with components $a_{1}, \ldots, a_{m}$ and $b_{1}, \ldots, b_{p}$. Can you multiply $\boldsymbol{a}$ times $\boldsymbol{b}^{\mathrm{T}}$ (yes or no)? What is the shape of the answer $\boldsymbol{a b}^{\mathrm{T}}$ ? What number is in row $i$, column $j$ of $a b^{\mathrm{T}}$ ? What can you say about $a a^{\mathrm{T}}$?

Neil Z. · Accepted Answer

Yes, you can multiply $a$ times $b^T$, the shape of the answer
$ab^T$ is $m$ by $p$. The number is row $i$, column $j$ of
$ab^T$ is $a_ib_j$

$aa^T$ is symmetric with the diagonal elements the squares of the
elements in $a$.

Exercise 1.2.2

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Exercise 1.2.2

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