學過線性代數的 進階參考書籍：

• "Applied Linear Algebra" (3rd ed) by Ben Noble & James Daniel
• "Applied Numerical Linear Algebra" (3rd ed) by James Demmel

重要觀念   &   指定練習    

第一章

§1.1 (none)
§1.2 # 1,2,3,5,7,8,9,11,13,16,17,18,20,21,22,23
§1.3 # 1,3,4,6,7,9,10,13,14,15,16,17,19,20,22,23,25,26,27,30,31,32
§1.4 # 3,4,6,9,11,12,13,14,15,19,21,23,26,27,28,30,32,37,38,39,40,41,43,45,48,52,55,57
§1.5 # 2,3,5,6,8,11,13,15,18,19,20,21,24,26,30,32,33,38,41,42,44,46,48
§1.6 # 2,3,6,8,11,13,15,17,19,20,21,22,23,24,25,30,32,41,49,51,57,58,68

第二章

§2.1 #1,2,4,6,8,9,10,13,14,16,17,19,25,27,29
§2.2 #3,5,10,14,15,16,19,21,22,27,31,38,41,43,48,52,53,54,56,57,61,64,67
§2.3 #3,5,6,9,10,14,16,17,19,21,25,27,28,30,32,33,36,37,41
§2.4 #4,8,9,10,15,16,17,21,23,25,27,32,37,40
§2.6 #4,5,6,11,13,16,17,23,25,26,28,29,30,31,35,36,40,43,47,48,50

期中考解答

第三章

§3.1 #6,12,15,16,19,20,25,26,33,37,38,40,42,43,45,52

§3.2 #2,7,8,13,14,18,20,24,25

§3.3 #7,8,10,14,16,17,21,22,25,27,29,32,33,36

§3.4 #2,3,7,8,12,13,14,17,19,22,24,25,27,28,31

第四章

§4.1 (none)

§4.2 #2,8,10,12,14,17,22,29

§4.3 #1,4,6,9,15,20,34,36,39

§4.4 #6,9,10,12,13,15,18,21,22,23,31

期末考解答

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下學期

第五章

§5.1 #6,9,10,14,20,21,27,29,33,34,36,38

§5.2 #1,2,7,10,12,14,17,20,25,27,34,36,38,39,42   殺 A 多項式例子

§5.3 #2,4,5,6,7,8,9,(10,11,12,13),20,21,22,26(b),27 (比較 #24 和 §5.2 第 249 頁的 5F)。

§5.4 #10,11,18,22,24,26,29,35,36,39,42,43

複數空間 \({\Large\mathbb C}^n\) 的向量內積為何? 所謂夾角如何定義? 與實際吻合嗎? (視 \({\Large\mathbb C}^n\) 為 \({\Large\mathbb R}^{2n}\) ) Complex Eigenvalues、內積

§5.5 #1,4,5,6,7,9,13,14,15,18,20,22,24,28,32,34,35,36,39,40,41,43,44,46,48,49,50

有關 \(\Large\displaystyle e^{At}\) 可參見『常微分方程』之 『線性常微分方程組』

§5.6 #4,5,8,11,13,17,18,19,21,22,24,28,32,33,35,40,42   Generalized Eigenspace、 續 Generalized Eigenspace

Chapter 5 Review #9,10,13, 14\{(a)}, 15,16(ignore 2 by 2 Q), 17,20, 21(esp.(c)), 24,30   Jordan form 計算範例一、 Jordan form 計算範例二

期中考解答

第六章

§6.1 #3,5,9,12,14≒17,19,20,21,22(later)
你一定要會配方 (將二次齊次多項式寫成線性獨立的平方和／平方差,
即 \(\Large x^TAx=\pm(c_1^Tx)^2\pm\cdots\pm(c_r^Tx)^2\), \(\Large\{c_1,\cdots,c_r\}\) 線性獨立。 範例 、 用矩陣做配方的範例

§6.2 #12,24,5,7,10,11,12,13,15,16,18,19,20

§6.3 #6-13,15-23

§6.4 #2,4,5,6,7,10,11,12,13 Rayleigh Quotient Example

§6.5 (skip)

第七章

§7.1 (none)
§7.2 #4,5,8,9,10,11,12,13,18,19,20,23,25
§7.3 #2,3,8,9,14
§7.4 #5,6,7,9,13,14,15,17

期末考解答