04.2.1 Visualizing the Four Fundamental Spaces

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Advanced Linear Algebra: Foundations to Frontiers
Robert van de Geijn and Maggie Myers

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This is absolutely amazing, so clearly explained and simple

whowto
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This should literally be given to students on thefirst day of any LA class.

Teacher: Here's this diagram, you won't completely understand it yet but hold on to it and reference it as we go.

Rockyzach
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Well, I didn't get it from the first problem. so should I know the LU decompostion first to understand it.
If it were in the form of a normal matrix I could have solved it.

can anyone suggest please.

uphadhayay
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There unknown way to visualize subspace, or vector spaces.

You can stretching the width of the x axis, for example, in the right line of a 3d stereo image, and also get depth, as shown below.

L R

|____|


This because the z axis uses x to get depth. Which means that you can get double depth to the image.... 4d depth??? :O

p.s
You're good teacher!

VolumetricTerrain-hzci