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As I understand matrix vector multiplication, a matrix linearly transforms a vector because the columns of the matrix represent the basis vectors of the coordinate system to which the vector is being transformed.

During principle component analysis we transpose the feature vector and the original dataset before multiplying them together to form a new dataset of principle components. What is baffling me is that transposing the eigenvectors that make up the feature vector would seem to misalign these basis vectors of the new coordinate system. Why isn't this transposed alignment of the feature vector problematic?

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  • $\begingroup$ Its based on linear algebra (matrix) operations, so for vectors to multiply they need to be arranged perpendicularly, You apply the operations required to get the dimensions ordered in the appropriate way. $\endgroup$ – ReneBt Jul 19 at 10:48

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