Matrix Transpose and the Four Fundamental Subspaces
3Blue1Brown's Linear Algebra Videos: Essence of linear algebra
Geogebra (Used for making plots):
Relevant StackExchange Answer: https://math.stackexchange.com/a/37402
Also relevant Quora Answer: https://www.quora.com/What-is-the-geo...
Notes
[1] By "gives a sense", I mean contains vectors that can form an orthogonal basis for the components of the vectors not in the ranges.
[2] It isn’t really legal to plot R^2 and R^3 on the same set of axes like this, R^2 and R^3 are completely different spaces, but I’m showing them like this to provide some intuition and justification for all three parts of the SVD.
Geogebra (Used for making plots):
Relevant StackExchange Answer: https://math.stackexchange.com/a/37402
Also relevant Quora Answer: https://www.quora.com/What-is-the-geo...
Notes
[1] By "gives a sense", I mean contains vectors that can form an orthogonal basis for the components of the vectors not in the ranges.
[2] It isn’t really legal to plot R^2 and R^3 on the same set of axes like this, R^2 and R^3 are completely different spaces, but I’m showing them like this to provide some intuition and justification for all three parts of the SVD.
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