{"topic":{"id":4547,"title":"大一新生的线性代数学习的小想法","slug":"topic","categoryId":54,"createdAt":"2023-07-28 09:05:27.1","bumpedAt":"2024-12-03 07:54:43.237116","views":495,"postsCount":10,"highestPostNumber":11,"likeCount":6,"closed":false,"pinned":false,"pinnedGlobally":false,"pinnedAt":null,"pinnedUntil":null,"isBanner":false,"excerpt":"这门课太抽象，有些老师也讲得抽象。我感觉我大一学习的时候陷入到数字和符号的海洋里迷失了自我。我现在反思，应当从图形上地去理解，并且和数学分析中的多元函数微分结合，能更加直观。例如 positive-semidefinite 这个概念，书本上和老师上课时只是讲了讲数学公式，作业或者考试也是给你个矩阵，让你按照背诵的定义和规则去判定。然而如果从 linear 的情况类推到 quadratic，并且告诉你它和数学优化方法的关系，Hess…","deletedAt":null,"isAnonymous":false,"category":{"id":54,"name":"学术专区","slug":"academic","color":"9EB83B"},"author":{"id":1047,"username":"anonymous_coward_old","name":"Anonymous Coward Old","avatarUrl":"/uploads/image/43/32/4332638c11248b8ff07033c11de0759a55205facfbec85e14458245a91991faf.avif"},"tags":["study","math","linear-algebra"]},"posts":[{"id":8117,"postNumber":1,"raw":"这门课太抽象，有些老师也~~讲得~~抽象。我感觉我大一学习的时候陷入到数字和符号的海洋里迷失了自我。\n\n我现在反思，应当从图形上地去理解，并且和数学分析中的多元函数微分结合，能更加直观。\n\n例如 positive-semidefinite 这个概念，书本上和老师上课时只是讲了讲数学公式，作业或者考试也是给你个矩阵，让你按照背诵的定义和规则去判定。\n\n然而如果从 linear 的情况类推到 quadratic，并且告诉你它和数学**优化**方法的关系，Hessian 的不同 definite 的情况对应不同的 optimization landscape，那会学起来有趣得多。\n\n[grid mode=\"tile\"]\n![_Optimization Basics uITNXWHZ1qQ-03|690x388](/uploads/image/30/c5/30c59d1945f86e30a3b8b6745e040a2fb544d29d20b7e91cde2ac9b3fbf1fbdc.avif)\n\n\n\n![_Optimization Basics uITNXWHZ1qQ-02|690x388](/uploads/image/75/6a/756a70fb925381bf1dd5e24fbd4370cd56a2a88c7823e189cab67ffae373d9a5.avif)\n[/grid]","cooked":"

这门课太抽象，有些老师也讲得抽象。我感觉我大一学习的时候陷入到数字和符号的海洋里迷失了自我。

我现在反思，应当从图形上地去理解，并且和数学分析中的多元函数微分结合，能更加直观。

例如 positive-semidefinite 这个概念，书本上和老师上课时只是讲了讲数学公式，作业或者考试也是给你个矩阵，让你按照背诵的定义和规则去判定。

然而如果从 linear 的情况类推到 quadratic，并且告诉你它和数学优化方法的关系，Hessian 的不同 definite 的情况对应不同的 optimization landscape，那会学起来有趣得多。

$\"_Optimization$

\n","createdAt":"2023-07-28 09:05:27.291755","updatedAt":"2024-03-17 13:05:01.741422","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":211,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":4,"publicVersion":4,"deletedAt":null,"isAnonymous":false,"user":{"id":1047,"username":"anonymous_coward_old","name":"Anonymous Coward Old","avatarUrl":"/uploads/image/43/32/4332638c11248b8ff07033c11de0759a55205facfbec85e14458245a91991faf.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":8154,"postNumber":2,"raw":"但是这些东西大部分一年级本科生一学期之内不太能能消化的了","cooked":"

但是这些东西大部分一年级本科生一学期之内不太能能消化的了

\n","createdAt":"2023-07-28 09:34:58.103921","updatedAt":"2023-07-28 09:34:58.103921","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":28,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":991,"username":"Siyuan","name":"Siyuan Wu","avatarUrl":"/uploads/image/7e/87/7e87136b5ed7cec7b65929e40d5f4a7be35578a674bc7f3cfafffcdad2783215.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":8155,"postNumber":3,"raw":"听交老师讲课基本就是浪费生命。。。讲习题可以稍微注意一下\n教材也挺烂的。。。当然后面还会有语言更抽象的教材。\n可以先看看 3b1b 的线性代数的本质，讲的很简单，还有可视化。https://www.bilibili.com/video/BV1ys411472E 四到八倍速溜一遍即可。\n然后看 Gilbert Strang 的经典课程 https://www.bilibili.com/video/BV18K4y1R7MP\n然后就是做书上的习题，偶尔注意一下老师讲的习题。考前做试卷，熟悉题型和考试范围，和书上习题挺多重合的，而且考的没什么难的。","cooked":"

听交老师讲课基本就是浪费生命。。。讲习题可以稍微注意一下
\n教材也挺烂的。。。当然后面还会有语言更抽象的教材。
\n可以先看看 3b1b 的线性代数的本质，讲的很简单，还有可视化。【官方双语/合集】线性代数的本质 - 系列合集四到八倍速溜一遍即可。
\n然后看 Gilbert Strang 的经典课程麻省理工Gilbert Strang教授线代大师-线性代数（全）
\n然后就是做书上的习题，偶尔注意一下老师讲的习题。考前做试卷，熟悉题型和考试范围，和书上习题挺多重合的，而且考的没什么难的。

\n","createdAt":"2023-07-28 09:40:54.799155","updatedAt":"2023-07-28 09:40:54.799155","replyToPostNumber":null,"replyCount":1,"likeCount":3,"wordCount":159,"liked":false,"bookmarked":false,"polls":[],"reactions":[{"reaction":"plus1","count":1,"users":[{"id":5905,"username":"PipaQinse233","name":"PipaQinse233"}],"hasReacted":false},{"reaction":"❤️","count":3,"users":[{"id":513,"username":"Grazure","name":"灰蓝天"},{"id":888,"username":"ghost","name":null},{"id":5905,"username":"PipaQinse233","name":"PipaQinse233"}],"hasReacted":false}],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":425,"username":"Ogiso_Setsuna","name":"小木曽雪菜","avatarUrl":"/uploads/image/84/e3/84e328169491dbc81e9b54386b259ed63a8e6678875dcf17803ec69c4c25cb99.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":8156,"postNumber":4,"raw":"我是考前一周刷完了 3b1b 的视频，然后直接刷题。最后也归功于考试题很简单，95+","cooked":"

我是考前一周刷完了 3b1b 的视频，然后直接刷题。最后也归功于考试题很简单，95+

\n","createdAt":"2023-07-28 10:04:51.333873","updatedAt":"2023-07-28 10:04:51.333873","replyToPostNumber":null,"replyCount":0,"likeCount":1,"wordCount":34,"liked":false,"bookmarked":false,"polls":[],"reactions":[{"reaction":"❤️","count":1,"users":[{"id":513,"username":"Grazure","name":"灰蓝天"}],"hasReacted":false}],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":31,"username":"TsuinoSora","name":null,"avatarUrl":"/uploads/image/77/06/7706643ba6d3ee1ec9d0070db0ad8a22bed8651fa8eb829cf44df4d20fa24b3b.avif","admin":false,"moderator":true,"signatureRaw":null,"signatureCooked":null}},{"id":8157,"postNumber":5,"raw":"我大一的时候刚接触线性代数，就被大量抽象的定义打败了，教材看了一遍也不会做题 :dizzy_face:","cooked":"

我大一的时候刚接触线性代数，就被大量抽象的定义打败了，教材看了一遍也不会做题 😵

\n","createdAt":"2023-07-28 10:14:02.509584","updatedAt":"2023-07-28 10:14:02.509584","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":39,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":307,"username":"Fast","name":null,"avatarUrl":null,"admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":8158,"postNumber":6,"raw":"这边建议直接看李永乐。","cooked":"

这边建议直接看李永乐。

\n","createdAt":"2023-07-28 11:10:25.460722","updatedAt":"2023-07-28 11:10:25.460722","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":11,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":543,"username":"Valencia","name":"Valencia","avatarUrl":null,"admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":8163,"postNumber":7,"raw":"我感觉抽象简洁的定义反倒比这些例子好掌握","cooked":"

我感觉抽象简洁的定义反倒比这些例子好掌握

\n","createdAt":"2023-07-28 12:14:46.589765","updatedAt":"2024-04-07 08:33:47.594659","replyToPostNumber":null,"replyCount":0,"likeCount":0,"wordCount":20,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":1047,"username":"anonymous_coward_old","name":"Anonymous Coward Old","avatarUrl":"/uploads/image/43/32/4332638c11248b8ff07033c11de0759a55205facfbec85e14458245a91991faf.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":8164,"postNumber":8,"raw":"当然学校的教材的材料组织的并不好，我看的 [Linear Algebra Done Right | SpringerLink](https://link.springer.com/book/10.1007/978-3-319-11080-6)","cooked":"

当然学校的教材的材料组织的并不好，我看的 Linear Algebra Done Right | SpringerLink

\n","createdAt":"2023-07-28 12:15:38.116636","updatedAt":"2024-04-07 08:33:47.678394","replyToPostNumber":null,"replyCount":0,"likeCount":1,"wordCount":26,"liked":false,"bookmarked":false,"polls":[],"reactions":[{"reaction":"❤️","count":1,"users":[{"id":5905,"username":"PipaQinse233","name":"PipaQinse233"}],"hasReacted":false}],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":1047,"username":"anonymous_coward_old","name":"Anonymous Coward Old","avatarUrl":"/uploads/image/43/32/4332638c11248b8ff07033c11de0759a55205facfbec85e14458245a91991faf.avif","admin":false,"moderator":false,"signatureRaw":null,"signatureCooked":null}},{"id":43936,"postNumber":10,"raw":"狠狠点了，3b1b 的可视化系列都很不错，尤其是这些基础学科，为了这我不惜把这个挖坟挖上来）相对论我也是在 3b1b 那看的，看完有一种洞见世界真相的错觉（×）\n\n总之对于大多数上手就觉得线性代数很抽象的同学，很推荐看看这里 3b1b 的视频","cooked":"

狠狠点了，3b1b 的可视化系列都很不错，尤其是这些基础学科，为了这我不惜把这个挖坟挖上来）相对论我也是在 3b1b 那看的，看完有一种洞见世界真相的错觉（×）

总之对于大多数上手就觉得线性代数很抽象的同学，很推荐看看这里 3b1b 的视频

\n","createdAt":"2024-12-03 07:41:23.061735","updatedAt":"2024-12-03 07:41:23.061735","replyToPostNumber":3,"replyCount":1,"likeCount":1,"wordCount":102,"liked":false,"bookmarked":false,"polls":[],"reactions":[{"reaction":"❤️","count":1,"users":[{"id":5905,"username":"PipaQinse233","name":"PipaQinse233"}],"hasReacted":false}],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":513,"username":"Grazure","name":"灰蓝天","avatarUrl":"/uploads/image/87/9a/879a08890144d8074d708625f4558ec8eb0cc8225467a769850aede5355e7afe.avif","admin":false,"moderator":false,"signatureRaw":"[right]——他乘长空的风，他是骄傲的鹰。[/right]","signatureCooked":"

——他乘长空的风，他是骄傲的鹰。

"}},{"id":43937,"postNumber":11,"raw":"3b1b 的内容确实好","cooked":"

3b1b 的内容确实好

\n","createdAt":"2024-12-03 07:54:43.237116","updatedAt":"2024-12-03 07:54:43.237116","replyToPostNumber":10,"replyCount":0,"likeCount":0,"wordCount":7,"liked":false,"bookmarked":false,"polls":[],"reactions":[],"wiki":false,"version":1,"publicVersion":1,"deletedAt":null,"isAnonymous":false,"user":{"id":5905,"username":"PipaQinse233","name":"PipaQinse233","avatarUrl":"/uploads/image/f7/1b/f71bbda87a32de08df517fe7ee4a14e3f63bfd1b2105d3ddb8ba1f4c2eaa1c29.avif","admin":false,"moderator":false,"signatureRaw":"[right]——發自我的手機[/right]","signatureCooked":"

——發自我的手機

"}}],"hasMore":false,"lastReadPostNumber":1,"hasUrlPostNumber":false}