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向量：建立线性代数的第一份直觉
学习资料
播放器下方提供英文笔记、测验、闪卡和 PPT 大纲。
PPT 资料为文字大纲，尚非完整演示文稿。
视频概览
3Blue1Brown《线性代数的本质》系列第一章，通过几何动画介绍向量，为从基础建立线性代数直觉开启学习路线。
HN 讨论的原因
HN 经常推荐用它建立线性代数直觉。评论认为它能帮助理解抽象概念，也适合与教材配合学习。
观看前准备
无需高等数学基础，熟悉坐标会有帮助。这节短课适合想在代数计算前建立几何直觉的学习者。
学习建议
分别用箭头和分量列表表示同一个向量，解释移动箭头时哪些性质不变。进入下一章前，用练习题检验自己是否理解这种区别。
最新优先
所在讨论： Immersive Linear Algebra Book with Interactive Figures
3Blue1Brown[1] has opened my eyes on the intuitive understanding of linear algebra, many, many years after taking a first course in linear algebra, which left me completely mystified. [1] [VIDEO]
所在讨论： An Illustrated Introduction to Linear Algebra, Chapter 2: The Dot Product
If you actually want to learn linear algebra, don't use this blogpost. It's real weaksauce compared to the wealth of free information and resources available online. Firstly, the real illustrated guide to linear algebra is the youtube series "The Essence of linear algebra" by 3blue1brown[1]. It has fantastic visualisations for building intuition and in general is wildly superior to this, which seems fine but…If you actually want to learn linear algebra, don't use this blogpost. It's real weaksauce compared to the wealth of free information and resources available online. Firstly, the real illustrated guide to linear algebra is the youtube series "The Essence of linear algebra" by 3blue1brown[1]. It has fantastic visualisations for building intuition and in general is wildly superior to this, which seems fine but extremely superficial. If you're done with 3b1b and want to take things further, then the go-to is the excellent 18.06SC course by the late and legendary Gilbert Strang. It's amazing, it's free. [2] Still want more? OK now you're talking my language. If you are serious about linear algebra (Up to graduate level, after that you need something else) then you want the book "Linear Algebra Done Right" by Sheldon Axler. It's available for free from the author's website[3] and he has made a bunch of videos to supplement the book. There's also an RTD Math full lecture series[4] that follows the book and he explains each thing in a lot of detail (because Axler goes fast , so it's beneficial to unpack the concepts a bit sometimes). [1] [VIDEO] [2] [LINK] [3] [LINK] and [LINK] [4] [LINK]
所在讨论： Adventures in Probability
The entire 3blue1brown series[0] on linear algebra is well worth watching, it has really intuitive graphical explanations of a bunch of concepts. Here's the one on determinants in particular[1]. TL;DW the determinant represents how much you scale the area/volume/hypervolume (depending on dimension) of a shape by applying a matrix transformation to each point. [0] [VIDEO] [1] [LINK]
所在讨论： Linear Algebra Done Right [pdf]
Linear Algebra Done right did not help me try to demystify linear algebra. Quite the contrary. It is the Youtube channel 3Blue1Brown[1] that gave me an intuition of what linear algebra was about, and I am forever thankful to him. Watch it and if you are a teacher, don't be a smug "formalist". [1] [VIDEO]
所在讨论： How do I relearn mathematics for machine learning?
3blue1brown's visualizations made a lot of things click for me, years after learning algebra and calculus. In my opinion they're the perfect companion to a more formal study with textbooks. Playlist for linear algebra: [VIDEO]
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