Linear Algebra 28 | Conservation of Dimension

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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)

[hopelesssuprem]

I watched the entire playlist on linear algebra in 3 days and I won't get tired of repeating that it was great. Now I am studying machine learning on my own and I had a few gaps, but now there are fewer of them. Thank you very much for such wonderful and most importantly necessary videos. I look forward to SVD in English)

[lexinwonderland]

I'm clicking through your other courses (such as this one) while waiting for an update to manifolds/topology, and as always your content is fantastic! I'm tempted to learn German just so I can keep up with more of your content!

[hyperduality]

Injective is dual to surjective synthesizes bijective or isomorphism.
Thesis is dual to anti-thesis creates the converging thesis or synthesis -- the time independent Hegelian dialectic.
Being is dual to non being creates becoming -- Plato's cat.
Alive is dual to not alive -- Schrodinger's cat.
"Always two there are" -- Yoda.

[maar]

I understood the whole video but did not understand the proof at 8:38. You used the compositions to define the inverse mapping. We know there is a linear mapping from U to V and for it to be bijective there should be a linear mapping from V to U and you use the composition of functions to prove it. But I dont see it quite clearly. Have we defined what composition of function means? Or is it already understood property like the properties of real numbers that we use in the proofs?