Algebraic and Analytic Geometry
《Algebraic and Analytic Geometry》 · 第 377 页 · Section 6.4「Normal and Self-Adjoint Operators」，Exercises 前的 Definitions（供习题 17–23 使用）
Definitions. A linear operator $T$ on a finite-dimensional inner product space is called positive definite [positive semidefinite] if $T$ is self-adjoint and $\langle T(x),x\rangle>0$ [$\langle T(x),x\rangle\ge0$] for all $x\ne0$ [for all $x$]. An $n\times n$ matrix $A$ with entries from $\mathbb R$ or $\mathbb C$ is called positive definite [positive semidefinite] if $L_A$ is positive definite [positive semidefinite].