This work is divided into four sections. The first section corresponds to the classical theoretical foundation of harmonic analysis with wavelets; it is used for clarity only. The second section presents the construction of the Discrete Wavelet Transform for vectors and its Inverse, emphasizing on storage efficiency. The third section presents the generalization of the Transform to matrices. It is equivalent to section 2, but some methods and tools used are slightly different, showing an alternative approach to the subject. The fourth section presents the main results of this work.

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