第3章 章节3A 练习3A.1 题目: Suppose \( b, c \in \mathbf{R} \). Define \( T: \mathbf{R}^3 \to \mathbf{R}^2 \) by \( T(x, y, z) = (2x - 4y + 3z + b, 6x + cxyz) \). Show that \( T \) is linear if and only if \( b = c = 0 \). 证明: 必要
第2章 章节2A 练习2A.1 题目: Find a list of four distinct vectors in \( \mathbf{F}^3 \) whose span equals \( \{ (x, y, z) \in \mathbf{F}^3 : x + y + z = 0 \} \). 解答: 任意\( (x, y, z) \in \{ (x, y, z) \in \mathbf{F}^3 : x + y + z
第1章 章节1A 练习1A.1 题目: Show that \( \alpha + \beta = \beta + \alpha \) for all \( \alpha, \beta \in \mathbf{C} \). 证明: \( \forall \alpha, \beta \in \mathbf{C} \),有\( \exists a, b, c, d \in \mathbf{R} \),使得\( \alpha = a + bi, \beta
第1章 章节1.1 练习1.1.1 题目: Prove Lemma 1.1.1. Lemma 1.1.1的内容: Let \( (x_n)_{n = m}^{\infty} \) be a sequence of real numbers, and let \( x \) be another real number. Then \( (x_n)_{n = m}^{\infty} \) converges to \( x \) if and only if \( \lim_{n \to
第23章 章节23.4 练习23.4.1 题目: Using the typing rules in Figure 23-1, convince yourself that the terms above have the types given. \[ \begin{aligned} &\text{id} = \lambda \text{X. } \lambda \text{x}: \text{X. } \text{x}; \\ \blacktriangleright \text{ } &\text{id} : \forall \text{X. } \text{X} \to \text{X} \end{aligned} \] \[ \begin{aligned} &\text{id} \text{ } [\text{Nat}];
正文 用 Quaternion 做旋转有省空间、连续多个 Quaternion 旋转和矩阵一样可以复合成单个 Quaternion 、复合操作的计算量比矩阵少、不受 Gimbal Lock 影响、更容易做插值等特点,因此在图形学领