Linear Transformations

Kernel, image, rank-nullity, and change of basis

Now that you know matrices are transformations, this module digs deeper: what gets sent to zero (the kernel), what the transformation can produce (the image), and the fundamental rank-nullity theorem that connects them. You'll also learn change of basis -- the technique behind diagonalization, PCA, and every 'feature extraction' pipeline in ML. Mini-lab: Compute the kernel and image of a transformation, verify the rank-nullity theorem, and perform a change of basis.

Estimated time: 60 minutes

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