Linear Algebra 28 | Conservation of Dimension [dark version]

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)

[Hunteriwi]

I have a question here, which I found is not so obvious.
Why is the linear map f: U -> V linear?
you take a step where you do f(x) = f(a_1*u_1 + ... + a_k*u_k) = a_1*f(u_1) + ... + a_k*f(u_k)
Why are you able to do this?
Weren't you supposed to say that since f(x) is in V, there exists unique b_i in R such that f(x) = b_1*v_1 + ... + b_k*v_k and then go through some algebra to the linearity?
Did I miss something there?
Glad I found this channel, I studied mathematics engineering and now I'm in the pedagogy area and I find these videos useful to remember some of the more abstract math I learned before.

[emiliograndinetti]

It's not exactly clear to me, how infectivity implies linear independence...