Dot products and duality | Chapter 9, Essence of linear algebra

Why the formula for dot products matches their geometric intuition. Help fund future projects:   / 3blue1brown   An equally valuable form of support is to simply share some of the videos. Home page: https://www.3blue1brown.com/ Dot products are a nice geometric tool for understanding projection. But now that we know about linear transformations, we can get a deeper feel for what's going on with the dot product, and the connection between its numerical computation and its geometric interpretation. Full series: http://3b1b.co/eola Future series like this are funded by the community, through Patreon, where supporters get early access as the series is being produced. http://3b1b.co/support Thanks to these viewers for their contributions to translations Hebrew: Omer Tuchfeld Vietnamese: @ngvutuan2811 ------------------ 3blue1brown is a channel about animating math, in all senses of the word animate. And you know the drill with YouTube, if you want to stay posted about new videos, subscribe, and click the bell to receive notifications (if you're into that). If you are new to this channel and want to see more, a good place to start is this playlist: https://goo.gl/WmnCQZ Various social media stuffs: Website: https://www.3blue1brown.com Twitter:   / 3blue1brown   Patreon:   / 3blue1brown   Facebook:   / 3blue1brown   Reddit:   / 3blue1brown