Question

What do you mean by positive form, negative form? Define these with example ( inner product space)

Answer 1

Positive form:

for any $u\isin V$, $(u,u)\ge0$

For example:

$u=(1,2,3)$

$(u,u)=1+4+9=14>0$

Negative form:

for any $u\isin V$, $(u,u)\le0$

For example:

$u=(i,2i,3i)$

$(u,u)=-1-4-9=14<0$