This Python3 implementation is in two parts.

Find eigenvectors of matrix

Calculates eigenvectors & eigenvalues of a symmetric matrix from scratch.

• uses Householder reflections to convert the matrix to Hessenberg form
• uses repeated Givens rotations to QR decompose the matrix, together with Wilkinson shift to speed convergence
• runtime should be a few seconds

I have included a theory document explaining as simply as possible the logic behind these matrix calculations, which was written for my own interest.

Compress image using eigenvectors

Case study implements the matrix calculations.

• imports 512x512 pixel photo
• decomposes into matrices of 512 eigenvectors & eigenvalues
• takes n most significant eigenvectors (initially n=128)
• projects image onto significant eigenvectors, resulting in principal component matrix, which represents the image in compressed form
• rebuilds an image from the compressed form
• calculates noise difference between original and rebuilt photo - which results in a peak signal to noise ratio of about 36 dB (within the range of 30-50 dB usually considered reasonable for compression)

Part 1 could be replaced with numpy.linalg.eig, if you are only interested in the image decomposition.

ENDS