Let V {\displaystyle {}V} be a finite-dimensional real vector space, endowed with a symmetric bilinear form ⟨ − , − ⟩ {\displaystyle {}\left\langle -,-\right\rangle } of type ( p , q ) {\displaystyle {}(p,q)} . Show that the negated form − ⟨ − , − ⟩ {\displaystyle {}-\left\langle -,-\right\rangle } has the type ( q , p ) {\displaystyle {}(q,p)} .
