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https://www.khanacademy.org/math/linear-algebra/alternate-bases/change-of-basis/v/linear-algebra-change-of-basis-matrixUsing a change of basis matrix to get us from one coordinate system to another.
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https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/lin-alg-invertible-change-of-basis-matrix?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebraMissed the previous lesson?
https://www.khanacademy.org/math/linear-algebra/alternate_bases/change_of_basis/v/linear-algebra-coordinates-with-respect-to-a-basis?utm_source=YT&utm_medium=Desc&utm_campaign=LinearAlgebraLinear Algebra on Khan Academy: Have you ever wondered what the difference is between speed and velocity? Ever try to visualize in four dimensions or six or seven? Linear algebra describes things in two dimensions, but many of the concepts can be extended into three, four or more. Linear algebra implies two dimensional reasoning, however, the concepts covered in linear algebra provide the basis for multi-dimensional representations of mathematical reasoning. Matrices, vectors, vector spaces, transformations, eigenvectors/values all help us to visualize and understand multi dimensional concepts. This is an advanced course normally taken by science or engineering majors after taking at least two semesters of calculus (although calculus really isn't a prereq) so don't confuse this with regular high school algebra.
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https://www.youtube.com/subscription_center?add_user=khanacademyAbout the Site 🌐
This site provides links to random videos hosted at YouTube, with the emphasis on random. 🎥
Origins of the Idea 🌱
The original idea for this site stemmed from the need to benchmark the popularity of a video against the general population of YouTube videos. 🧠
Challenges Faced 🤔
Obtaining a large sample of videos was crucial for accurate ranking, but YouTube lacks a direct method to gather random video IDs.
Even searching for random strings on YouTube doesn't yield truly random results, complicating the process further. 🔍
Creating Truly Random Links 🛠️
The YouTube API offers additional functions enabling the discovery of more random videos. Through inventive techniques and a touch of space-time manipulation, we've achieved a process yielding nearly 100% random links to YouTube videos.
About YouTube 📺
YouTube, an American video-sharing website based in San Bruno, California, offers a diverse range of user-generated and corporate media content. 🌟
Content and Users 🎵
Users can upload, view, rate, share, and comment on videos, with content spanning video clips, music videos, live streams, and more.
While most content is uploaded by individuals, media corporations like CBS and the BBC also contribute. Unregistered users can watch videos, while registered users enjoy additional privileges such as uploading unlimited videos and adding comments.
Monetization and Impact 🤑
YouTube and creators earn revenue through Google AdSense, with most videos free to view. Premium channels and subscription services like YouTube Music and YouTube Premium offer ad-free streaming.
As of February 2017, over 400 hours of content were uploaded to YouTube every minute, with the site ranking as the second-most popular globally. By May 2019, this figure exceeded 500 hours per minute. 📈
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