Amendment to the result on the trace of Haar wavelets matrix

Document Type : Research Paper


Department of Studies in Mathematics, V. S. K. University, Ballari-583105, INDIA.



    Trace and some other interesting properties of Haar wavelets matrix of size $2^K$ are studied by Shiralashetti and Kumbinarasaiah \cite{ref6}, results related to the trace of Haar wavelets  matrix derived based on $K$ is even or odd and the same is concluded in Theorem $3.2$. This article deals with the trace of Haar wavelets matrix in depth by identifying and overcoming the pitfalls occur in the proof of Theorem 3.2.


[1] C.F. Chen and C.H. Hsiao, Haar wavelet method for solving lumped and distributed parameter systems, IEE Proc., Control Theory Appl., 144 (1997), 87-94.
[2] A. Haar, Zur theorie der orthogonalen Funktionsysteme, Math. Ann., 69 (1910), 331-371.
[3] G. Hariharan and K. Kannan, An overview of Haar wavelet method for solving differential and integral equations, World Applied Sciences Journal, 23(12) (2013), 01-14.
[4] U. Lepik and H. Hein, Haar Wavelets With Applications,  Springer International publishing, 2014.
[5] P. Porwik and A. Lisowska, The Haar–Wavelet transform in digital image processing : Its status and achievements, Machine GRAPHICS and VISION, 13(1/2) (2004), 79-98.
[6] S.C. Shiralashetti and S. Kumbinarasaiah, Some results on Haar wavelets matrix through linear algebra, Wavel. Linear Algebra, 4(2) (2017), 49-59.