#### [[videos_Linear algebra_3Blue1Brown]] **Creator**:: [[3Blue1Brown]] **Source**:: [](https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw) **Covers**:: - [Chapter 1](https://www.youtube.com/watch?v=fNk_zzaMoSs&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=1) - [[Linear algebra revolves around vector addition and scalar multiplication]] - [[Scalar]]s numbers used to scale vectors. - [[Vector]] - a numerical representation of a direction and distance ([[Computer Science|CS]] perspective), or a visual representation of a value of a movement on multiple axis ([[physics]] perspective) - [Chapter 2](https://www.youtube.com/watch?v=k7RM-ot2NWY&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=2) - [[i-hat]] and [[j-hat]] => x and y vectors of length one which are the basis [[Vector]]s of the xy coordinate system - linearly independent values represent all values and linearly dependent represent limited values - [09:00](https://www.youtube.com/watch?v=k7RM-ot2NWY&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=2#t=540.477331) - Basis of a vector space is a set of linearly independent vectors that span the full space - Span of two vectors is th set of all their linear comvinations [04:24](https://www.youtube.com/watch?v=k7RM-ot2NWY&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab&index=2#t=264.340176) - ![[Pasted image 20211016232847.png]] - [Chapter 3](https://www.youtube.com/watch?v=kYB8IZa5AuE&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab) - linear transformation - transformation takes in inputs and spits out outputs (function) [00:55](https://www.youtube.com/watch?v=kYB8IZa5AuE&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab#t=55.947969) - linear = all lines must remain lines (not curves) and the origin is fixed [02:50](https://www.youtube.com/watch?v=kYB8IZa5AuE&list=PLZHQObOWTQDPD3MizzM2xVFitgF8hE_ab#t=170.039281) - this means that lines will remain parralel and evenly spaced - when calculating linear transformations all vectors will remain a linear combination of [[i-hat]] and [[j-hat]] - ![[Pasted image 20211016234528.png|locl]] - ![[Pasted image 20211016234602.png]] - ![[Pasted image 20211016234656.png|locr]]