What is semipositive definite?

[anbhadane]

In Jackson,(3rd edition) Chapter 1 , page no, 44 He uses the word "semipositive definite" what is it? is it "non-negative" definite?

 

[fresh_42]

It is usually called positive semidefinite unless Jackson didn't use something completely different. It means that for a bilinear real form: $\beta\, : \,\mathbb{R}^n\times \mathbb{R}^n\longrightarrow \mathbb{R}$ we have $\beta(v,v)=\langle v,v\rangle \geq 0$.

The essential difference to a usual inner product (positive definite) is, that there may be vectors $v\neq 0$ such that $\beta(v,v)=0$.

 

[anbhadane]

Oh, Thank you, got it.