Matrix multiplication, PCA

Course Q&A Math for Machine Learning Linear Algebra for Machine Learning and Data Sc...
1

in the matrix multiplication AB, are these two statements correct?

  1. we transform matrix B by matrix A
  2. we project matrix A to matrix B
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2

Dear @flyunicorn,

:check_mark: Correct — In AB, matrix A applies a transformation to B (specifically, to B’s columns).
:multiply: Incorrect — Matrix multiplication does not imply projection. Projection has a specific meaning unrelated to standard AB multiplication.

–
Keep Learning AI with DeepLearning.AI - Girijesh

3

But in the PCA video, it seems a matrix one the left is projected to the matrix on the right.

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4

Yes, in PCA, the matrix on the left (original data) is projected onto the matrix on the right (principal components).

–
Keep Learning AI with DeepLearning.AI - Girijesh

5

In effect, when you take the dot product of your data matrix and the eigenvector matrix - you are projecting the matrix on the principle components.

When you get to the coding exercise - this is a dot product of the dataset and the matrix composed of the eigenvectors (the principle components)

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