Linear Algebra 21 : 4 Fundamental Subspaces

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In this video I cover the 4 Fundamental Subspaces being the Null Space, Column Space, Row Space and Left Null Space. I will be showing why they are important in upcoming videos.

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ALGEBRA YOU NEED TO KNOW

Linear Algebra is an essential branch of mathematics in the fields of chemistry, computer graphics, physics, economics, statistics, machine learning, engineering, etc.

It is used to model many types of natural phenomena, create unbreakable cryptography algorithms, maximize yield in agriculture, make stock market predictions, improve file compression, make complex calculations effortlessly and it is a core part of Google page rank.

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THANK YOU TO MY PATREON SUPPORTERS LIKE :

[maverick]

I think you messed up the order of the equation for the left null space.
(A^T x)^T = x^T A

Otherwise you won't get a valid multiplication. You cannot multiply an n×n matrix from the left to a row-vector (which is basically a 1×n matrix).

[OpCzar]

Derek's presentation is always top notch, no matter the subject!

[yasirdikbas]

Derek please keep up the good work you are awesome !

[rbc]

What is the purpose of learning subspace. Is there any significance?

[hameedyousfi]

Thanks alot sir if u upload tenserflow tutriol after this algebr then sir start a new series real project with m.l like you did with 12 videos series on javascript and i suggest like face recogniation 3d picture and aton of thing which you can do sir and again w8ing for your tututriol