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].

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Ordinary matrix-vector multiplication

**Physics Forums | Science Articles, Homework Help, Discussion**