準正定である.

09:19 Mar 10, 2015 

In that case "non-negative" is what you need. But isn't that usually 非負?

2次形式評価関数

2乗面積
x[正定性]
（１） が正定（準正定）
（２） のすべての固有値が正（非負）
（３）すべての主座小行列式が正（主小行列が非負）

06:00 Mar 10, 2015 

The expression defining z in the document is a long and complex equation, that is difficult to reproduce here, especially the mathematical symbols involved.
But it is definitely not a matrix equation, and the terms are all algebraic and (definite) integral expressions.

When I go further into the contents of the paper, I think I will have a clearer idea. As it is, 'non zero real number' appears to fit the context.
Thank you, DLyons, for your input.

05:04 Mar 10, 2015 

You're right about z, but isn't it saying that z is defined by a matrix condition?

Would "quasi-positive definite" work? Some more context would help.

04:58 Mar 10, 2015 

Aren't ' positive definite', ' positive semidefinite' the properties of matrices?
Here, z ∈ R, so it is a real number, not a matrix.
In this context, could it mean 'non negative', that is,≥0?

04:20 Mar 10, 2015 

半正定値
M が半正定値 (positive-semidefinite) または非負定値 (nonnegative-definite) であるとは、Cn の（実の場合は Rn の）任意の非零ベクトル x に対して z∗ Mz ≥ 0 が成り立つときに言う。