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In this video, we learn a very useful matrix trick called singular value decomposition (SVD), in which we express a matrix as a product of two rotation matrices and one scaling matrix.
We also show a very interesting application to image compression.

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Introduction: (0:00)
Transformations: (0:50)
A puzzle: (1:27)
A harder puzzle: (2:21)
Linear transformations: (3:50)
Dimensionality reduction: (10:50)
Image compression: (23:57)