Linear Algebra 21 | Examples of Linear Maps

Thanks to all supporters! They are mentioned in the credits of the video :)

This is my video series about Linear Algebra. I hope that it will help everyone who wants to learn about it.

#LinearAlgebra
#Vectors
#Matrices
#MachineLearning
#Eigenvalues
#Calculus
#Mathematics
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(This explanation fits to lectures for students in their first year of study: Mathematics for physicists, Mathematics for the natural science, Mathematics for engineers and so on)

[fatihakyildiz]

Julian, thank you very much for your effort. Your presentation of linear algebra is just great.

[hopelesssuprem]

it's a brilliant explanation. U know there is a famous 3bluebrown channel and I watched this and now I may confidently declare that your exmpanation of linear algebra is in 1000 times better.

[sinclairabraxas]

i love getting high and watching your videos I think at this point I've seen hundreds of them, they don't feel like higher maths at all, feels like you are telling a beautiful story

in Brazil we had a great mathematician and pedagogue called Elon Lages Lima, he studied German and consequently read a bunch of German analysis textbooks, he wrote dozens of textbooks, and 3 in particular, Curso de Análise vol 1 and vol 2, and Algebra Linear, read A LOT like your lectures, I guess that's why I love them so much, you can really tell the German influence on his material, if I find a translated pdf I will send them to you, the exercises are specially good, anyway it's awesome seeing how they teach it over there

thank you for your work, I will open a wine bottle and spend the next 4 hours watching you videos

[id-icou]

Nice! Do you plan to make a video about the singular value decomposition ?

[salimallami]

Thank you very much. I benefit greatly from the lessons. Can you explain the difference between a matrix and a linear map? Is there a philosophical difference or not? Thanks

[MrWater]

if it is not possible for a linear map to make subspaces bigger it means that n <= m, so we can have square matrices or wide matrices but not long matrices? But how does it related with the fact that linear map induces matrices? Because we can have matrices where m>n so..that matrices are not linear maps?