Let [tex]P=(p_{ij})[/tex] be a real symmetric 2x2 matrix. Show that the function on [tex]\mathbb{R}^2\times\mathbb{R}^2[/tex] (Where R^2 is a space of column vectors) defined by [tex]<v,w>=v^tPw[/tex] is an inner product if and only if [tex]p_{11}[/tex] and [tex]det(P)[/tex] are both swtrictly positive.(adsbygoogle = window.adsbygoogle || []).push({});

I just need to know what [tex]Pw[/tex] means in [tex]<v,w>=v^tPw[/tex].

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# Ordinary matrix-vector multiplication

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