Can we characterize the wavelets through linear transformation? the answer for this question is certainly YES. In this paper we have characterized the Haar wavelet matrix by their linear transformation and proved some theorems on properties of Haar wavelet matrix such as Trace, eigenvalue and eigenvector and diagonalization of a matrix.

Proof planning is a novel knowledge-based approach for proof construction, which supports the incorporation of mathematical knowledge and the common mathematical proof techniques of a particular mathematical eld. The diagonalization proof technique is a well-known method in theoretical computer science and in mathematics that originated with Can-tor, who used it to show his seminal uncountabili...

A coordinate transformation is found which diagonalizes the axisym-metric pp-waves. Its effect upon concrete solutions, including impulsive and shock waves, is discussed.