Linear Algebra 3d2: Decomposition in ℝⁿ, 2

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Words can't express how grateful and I am for this series of lessons.  You are a wonderful teacher, the best I have had.  I enjoy math again and understand the one thing math teachers in the past have seemed to neglect, Why. Why am I doing this, why does this happen and so on....    Thanks again,   I'd give you a hug if you where not inside my computer :)

EGHTY
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"One of your few favorite things, " right in the feels.

samdeschamps
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It's kinda like solving the Rubik's cube where you have solved one face and when you try solving another one, it messes up the first one ;) (that is, unless you do it more cleverly, with commutators and their conjugates).
Hmm.... but this makes me wonder: could there be a way to map the Rubik's cube problem to linear algebra problem and solve it by solving linear equations in some way? :>

alojzybabel